1. Find the derivative of \( \displaystyle g(x)=\int_{1}^{x} \sqrt[3]{ \sin{t}+ 7t^3 }\;dt \)

Solution

2. Find the derivative of \( \displaystyle h(x)= \int_{x}^{17} e^{\cos{t}}\sec{t} \;dt \)

Solution

3. Find the derivative of \( \displaystyle s(x)= \int_{3}^{\tan{x}} t^4e^{t^2+3t} \;dt \)

Solution

4. Find the derivative of \( \displaystyle p(x)=\int_{x^2}^{x^3+x} t^2+1 \;dt \)

Solution

5. Find \( \displaystyle \frac{d}{dx}\left(\int_{x}^{4} \frac{t^4-3t^3}{t^2+1} \;dt \right) \)

Solution

Evaluate the following definite integrals.

6. \( \displaystyle \int_{1}^{3} 2x-3x^2 + 1 \;dx \)

Solution

7. \( \displaystyle \int_{-1}^{1} (x-1)(x+1) \;dx \)

Solution

8. \( \displaystyle \int_{1}^{2}\frac{3x^2-2x^3+2}{2x^3} \;dx \)

Solution

9. \( \displaystyle \int_{-\frac{\pi}{4}}^{\frac{\pi}{3}} \sin{x} \;dx \)

Solution

10. \( \displaystyle \int_{0}^{1} \frac{2}{1+u^2} \;du \)

Solution