calculus questions and answers grade 12

Find the integral of (sec^2 x)/(sqrt(tan x)) dx. int (t + 3)2 / t3 dt. g(t) = t^2 - \dfrac {4}{t^3}, Compute the value of L{Hat} Y (theta, phi) for the function: 1/4pi^{1/2}, Evaluate the integral. Find f: f"(x) = -2 + 12x - 12x^2, f(0) = 4, f'(0) = 12. \int_4^8 {{{\sqrt {\ln x} } \over x}} dx. If r(t) = 20e^(0.02t), and if the tank contains 3000 gallons initially, find a formula for Q(t), the amoun... Find f. f'''\left( t \right) = {e^t} + {t^{ - 4}}, Find f. f''\left( x \right) = {2 \over 3}{x^{2/3}}. Find the derivative of y = cot(x) csc(x). Pump A is started at 8:00 a.m. and pump B is started at 10:00 a.m. At 12:00 p.m. 60% of the pool is empty when pump B broke down. int sec(t)(6 sec(t) + 7 tan(t)) dt. Password * The sum of the squares of the same terms is equal to 1092. f''(x) = 32x3 - 15x2 + 10x f(x) =, Determine the following antiderivative: int x3 x4 + 3 dx, Determine the following antiderivative: int (e3x + x3 + 3 sqrt x)dx, Evaluate the following: a. integral_1^3 integral_0^2 (y + x^2) dxdy b. integral_0^5 integral_0^2y (xy^2 - x^2)dxdy. Sciences, Culinary Arts and Personal Do not simplify with exception of multiplication of numbers. integral x^2 (x + 1)^2 dx. \int {y\sqrt {2 + 14y - 49{y^2}} } \ dy. A cat falls from a tree (with zero initial velocity) at time t = 0. Find the constants a and b so that all the 4 lines whose equation are given by. (Use C for the constant of integration.) Evaluate the integral \int_{1}^{3} (8 + 5x)\ dx by interpreting it in terms of area. 12th grade. \int \frac{x^2}{(2x + 1)(x + 2)^2}dx \\b). Find the volume of the region bounded above by the paraboloid z = 12 - x^2 - y^2 and below by the paraboloid z = 11x^2 + 11y^2. Find the area of the right triangle shown below. Evaluate the integral \int sec^{5}x\ tan^{3}x\ dx. Solve the following integrals: (A) The integral from 0 to 1 of x * sqrt(3x^2 + 2) dx, (B) the intergal of xe^(3x^2) dx. Use cylindrical coordinates to evaluate the integral where R is the cylinder x^2 + y^2 \leq 1 with 0 \leq z \leq 1. Give a clear and detailed solution of the integral of e^{-ct/m}, Differentiate. Should the firm increase th... Let f(x) = { 0 if x greater than -4 2 if -4 greater than equal to x greater than 1 -5 if 1 greater than equal to x greater than 5 0 if x less than equal to 5 and g(x) = Integral_{-4}^{x} f(t) dt. Work the integral. Evaluate int 12xe^x dx using integration by parts with u = 12x and dv = e^x dx. Check the answer by differentiation. Find f. f"(theta) = sin(theta) + cos(theta), f(0) = 2, f'(0) = 4, Find the integral by the substitution method. v(t) =... Find the indefinite integral: integral (x^3 + 4) dx. All rights reserved. Evaluate the definite integral 7 5 20 x 2 d x. If y = 0.75cos(3x), state the integral of y with respect to x. The number of boys in school B is 200 higher than the number of boys in school A. integral_0^4 integral_0^{y / 2} dx dy + integral_4^6 integral_0^{6 - y} dx dy. They each continue to the opposite bank, immediately turn around and start back to the other bank. integral_1^4 square root [5] u du. Evaluate the following definite integral. social sciences. Find y ' if y = … y = \sqrt[3]{x^2 + 9}, Evaluate the integral. Edit. Evaluate the integral: int 0 1 sqrt x2 + 1 dx. They first pass each other 1400 meters from one bank. In part B, a student must answer 6 of 8 questions and in part C, a student must answer all questions. Find the indefinite integral. If you are a teacher, you are encouraged to print and distribute paper based copies to your students. A factory produces bicycles at a rate of 100 + 0.1t^2 - 1.1t bicycles per week (t in weeks). Find the area of the region bounded by the graphs of the given equations. Calculus is built on the concept of limits, which will be discussed in this chapter. ), Find the integral. Use cylindrical coordinates to evaluate the triple integral \displaystyle \iiint_E\sqrt{x^2+y^2}\;dV, where E is the solid bounded by the circular paraboloid, Evaluate \int \dfrac{2x^4 -1}{\sqrt x}\ dx. 5 of the video are wrong. They cover all the major topics in the South African NCS curriculum such as calculus, algebra, functions, trigonometry. Integral (2x + 2)^3 dx. Evaluate the integral: the integral of (3x^2 + 6x - 5) dx. Favourite answer. Bounded by the curve y = \sqrt{x} , the x-axis , and the lines x = 0 and x = 4. Find the three terms of the sequence. Evaluate \int_{0}^{9}(ti + t^2j + t^3k) dt = \boxed{\space}i + \boxed{\space}j + \boxed{\space}k. Find \int \Bigg \frac{2}{x} + \frac{5}{x^3}\Biggdx . integral 1 / {x square root {25 x^2 - 1}} dx, Find the integral. Evaluate the integral using u-substitution. Evaluate the integral 64 1 1 + 3 x 7 x d x. 2) \int e^{x^3}x^2dx. Evaluate the following integral. Integral y^2 dy = Integral 2x dx, Evaluate the indefinite integral. (Use C for the constant of integration.) The ratio of the boys in school A and the boys in school B is 1:3 and the ratio of the girls in school A and the girls in school B is 3:5. (b) Use f(0) = 0 to evaluate the constant. Find k. A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). \int_{1}^{2} \frac{2x+2}{2x^2+x-1}dx, Evaluate the following integral. Integrate and simplify: the integral of (2/x + x/2) dx. Determine x = f(t) for (t^2 + 3t)\frac{dx}{dt} = 3x + 3,t 0; f(1) = 5. Calculate the dimensions of a rectangle with a perimeter of 312 m for which the area, V, is at a … integral 3 sinh (x / 3 - ln 2) dx (Use C as the arbitrary constant. \int \frac {dx}{\sqrt [4]{(x - 1)^3(x + 2)^5}}, Compute the integral. Twelfth Grade (Grade 12) Calculus questions for your custom printable tests and worksheets. Evaluate the indefinite integral. Exercises36 13. y = x^2, y = 4x - x^2. Evaluate \int_{4}^{9} \frac{2x+3}{\sqrt x} dx. Find f ( x ) such that f ( x ) = 2 x 2 + 3 x 3 and f ( 0 ) = 5 . 0% average accuracy. Find the number of boys and girls in each school. y = 5(7x^3 + 1)^{-3}, Calculate the derivative of the following function. To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Step-by-step solutions to all your Calculus homework questions - Slader. A particle moves in a straight line and has acceleration given by a(t) = 2t - 9. There will be no questions involving Integral Calculus on the final exam. The slope f prime (x) at each point (x, y) on a curve y = f(x) is given, along with a particular point (a, b) on the curve. Set up the limits for the triple integral on the region bounded by x2 + y2 + z2 = 4, x leq 0 and z leq 0. The flight of object propelled upward with no other forces acting on it travels with a velocity modeled by: v(t) = 120 -32t. Show work. Chapter: Di erential Calculus - Grade 12 1 Why do I have to learn this stu ? The velocity of a (fast) automobile on a straight highway is given by the function: V(t) = 3t if 0 less than or equal to t less than or equal to 20 60 if 20 less than or equal to t less than or eq... Find the volume of the solid enclosed by z = \sqrt{x^2 + y^2}, z =0, x^2 + y^2 = 25. Two Limits in Trigonometry36 14. Evaluate the integral integral_{-4}^{4}e dx. Evaluate the definite integral. Calculate the total area of the region described. x. x → x − 4 − 3 9 does not. 5 months ago. First sketch the graph of function 1 + sqrt(9 - x2), then evaluate the following definite integral by interpreting it in terms of an area: int -3 0 1 + sqrt(9 - x2)dx. Evaluate the integral by interpreting it in terms of areas. 900 seconds . A rock is dropped into a water well and it travels approximately 16t. In part B, a student must answer 6 of 8 questions and in part C, a student must answer all questions. Edit. Calculus is one of the central branches of mathematics and was developed from algebra and geometry. Evaluate the following indefinite integral. Find the average value of f(x, y) over the region R. f(x, y) = x^2 + y^2 R: square with vertices (0, 0), (4, 0), (4, 4), (0, 4). Also, please include the table that shows in picture 2(it's an example) for the local maximum and … Pramod Kumar. \int \frac{(t + 2)^2}{t^5}dt = \boxed{\space}. Evaluate the indefinite integral. Type only one variable. ( Use C for the constant of integration.)

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