Free AP Calculus AB Tests

AP Calculus AB Practice Tests

Logarithms
Limits
Derivatives Part 1
Derivatives Part 2
Derivatives Part 3
Idefinite & Definite Integrals
Riemann Sums, Trapezoidal…
Trigonometric Integrals
Applications of Calculus
Differential Equations

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AP Calculus AB Practice Test: Trigonometric Integrals

This free AP Calculus AB unit test covers trigonometric integrals, the second fundamental theorem, and areas between curves. Trig integrals on the AP exam will usually involve some kind of u-substitution. Additionally, when calculating the area between two functions, make sure you sketch out the given functions to identify the enclosed area.

Next: AP Calculus AB Applications of Calculus

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Free AP Calculus AB Tests

AP Calculus AB Practice Tests

More AP Calculus AB Practice Exam

AP Calculus AB Practice Test: Trigonometric Integrals

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1. Question

$\displaystyle\int \sin^3(x)dx$

2. Question

$\displaystyle\int \sin^2⁡(x)\cos^2⁡(x)dx$

3. Question

$\displaystyle\int \sec^4(x)\tan^4(x)dx$

4. Question

$\displaystyle\int \sec^3(x)\tan^3(x)dx$

5. Question

$\displaystyle\int \tan^3(x)dx$

6. Question

$\dfrac{d}{dx}\left(\displaystyle\int_0^{3x} 3t dt\right)$

7. Question

$\dfrac{d}{dx}\left(\displaystyle\int_0^{\cos(x)} \sin(t) dt\right)$

8. Question

$\dfrac{d}{dx}\left(\displaystyle\int_0^{x^2} \ln(t^2 + t)dt\right)$

9. Question

$\dfrac{d}{dx}\left(\displaystyle\int_0^{\frac{1}{x}} (3t + 5)dt\right)$

10. Question

$\dfrac{d}{dx}\left(\displaystyle\int_0^{x^7} \csc^2(3t)dt\right)$

11. Question

Find the area bounded by the functions $f(x) = x^2 + 3x + 2$ and $g(x) = x + 5$.

12. Question

Find the area bounded by the functions $f(x) = \cos(x)$ and $g(x) = x^2 + 3x$ on the interval $[π, 2π]$.

13. Question

Find the area between the functions $f(x) = x^2$ and $g(x) = x^3$ on the interval $[1, 3]$.

14. Question

Determine the area enclosed by the functions $x = y^2 − 3$ and $y = x + 1$.

15. Question

Determine the area enclosed by $f(x) = \cos⁡(x)$ and $g(x) = \sin⁡(x)$ on the interval $\left[0, \dfrac{π}{2}\right]$

Next: AP Calculus AB Applications of Calculus