Practice finding antiderivatives, evaluating definite integrals, and applying the Fundamental Theorem of Calculus.
Read each problem carefully. Show your work and include units when they are appropriate.
Finding antiderivatives and evaluating definite integrals
Math - Grade 9-12
- 1
Find an antiderivative of f(x) = 6x^2.
- 2
Find the indefinite integral integral of (4x^3 - 2x + 5) dx.
- 3
Evaluate integral from 0 to 3 of 2x dx.
- 4
Evaluate integral from 1 to 4 of (x + 2) dx.
- 5
Use the Fundamental Theorem of Calculus to find the derivative of F(x) = integral from 2 to x of (t^2 + 3) dt.
- 6
Use the Fundamental Theorem of Calculus to find the derivative of G(x) = integral from -1 to x of (5t^4) dt.
- 7
Find the value of integral from 0 to 2 of (3x^2 - 4) dx.
- 8
Find an antiderivative of f(x) = 1/x for x > 0.
- 9
Evaluate integral from 1 to e of (1/x) dx.
- 10
If F'(x) = 8x - 3, find one possible function F(x).
- 11
Evaluate integral from -2 to 2 of x^3 dx.
- 12
Find the average value of f(x) = x^2 on the interval [0, 3].
- 13
A particle moves with velocity v(t) = 3t^2 meters per second for 0 less than or equal to t less than or equal to 2. Find the displacement from t = 0 to t = 2.
- 14
Suppose H(x) = integral from 0 to x of (2t + 1) dt. Find H(3).
- 15
Evaluate integral from 2 to 5 of 7 dx.