Example problems

1. Evaluate these indefinite integrals:

(a) ${\displaystyle \int 2x^{5}\,dx}$

(b)${\displaystyle \int 7x^{6}+2x^{3}-x^{2}\,dx}$

2. Find the equation of the curve:

(a) Given ${\displaystyle {\frac {dy}{dx}}=x+5}$ and that the point (0, 3) lies on the curve.

(b) Given ${\displaystyle {\frac {dy}{dx}}=3x^{2}+7x+0.1}$ and that the point (2, 2) lies on the curve.

3. Evaluate these definite integrals

(a)${\displaystyle \int _{0}^{2}x+1\,dx}$

(b)${\displaystyle \int _{-3}^{4.7}{\frac {1}{7}}x^{\frac {1}{3}}+1\,dx}$

4. Find the area between the curve of ${\displaystyle y=-x^{4}-{\frac {1}{2}}x^{3}+3x^{2}}$ and the x-axis from x=-2 to x=0.

Worked solutions can be found here: Integration problem solutions