worksheet on integration
.....Optional test on 12/15. Final on 12/17.....

Find all the integrals. Be careful to include the constant of integration if needed. Don’t be afraid to use symmetry to help you out.

1. $\int (\sin x + \cos x) dx$

2. $\int (x^2 - 16x^3 + x^{-2}) dx$

3. $\int_0^1 (x^3 - x^2) dx$

4. $\int (x + x^3)/x^{1/3} dx$

5. $\int \frac{\sin(x)}{\cos^2(x)} dx$

6. $\int_0^2 2x(2x^2 + 4) dx$

7. $\int_{-\pi}^\pi (\sin x + \cos x) dx$

8. $\int_{-5}^5 x^3 dx$

9. $\int_0^4 x/\sqrt{2x+1} dx$

10. $\int_0^\pi \cos(2x/3) dx$

Find the derivatives

$$\frac{d}{dx} \int_{10}^x \sin(t^2) dt,\quad \frac{d}{dx} \int_{-10}^{x^2} \sin(t^2) dt$$