Fundamental Theorem of Calculus with Definite Integrals

Practice Questions

AP Calculus BC › Fundamental Theorem of Calculus with Definite Integrals

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1

Evaluate $\int_{0}^{6} (x-3)^2 dx$

2

Evaluate :

$f(x)=\int_{0}^{x} \sin\left(\sqrt{t^2+\frac{\pi^2}{4}} \right )dt$

3

$\int _{\frac{\pi}{3}} ^ {\pi } \sin (x/2) dx$

4

Suppose we have the function

$\small g(x)=\int_{0}^{\cos x}(1+\sin t)dt$

What is the derivative, $\small g'(x)$ ?

5

Evaluate when $f(x)=\int_{0}^{x}(2t^{2}+5t-4)dt$ .

6

$\int_{-1}^{3} \left (4x^2 - x \right )dx$

7

Given

$f(x)=\int_{0}^{x}(\frac{2}{t^{2}+4t-5})dt$ , what is ?

8

Given

$f(x)=\int_{0}^{x}\left(\frac{1}{t^{2}}-2t+3\right)dt$ , what is ?

9

Find the result:

$\frac{\mathrm{d} }{\mathrm{d} x} \int_{1}^{e^x} t \ln t ; \mathrm{d}t$

10

Evaluate when $f(x)=\int_{0}^{x}(6t^{2}-3t+10)dt$ .

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