A-level Mathematics/OCR/C2/Integration/Problems

Example problems

1. Evaluate these indefinite integrals:

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

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

2. Find the equation of the curve in each of the following cases:

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

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

3. Evaluate these definite integrals

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

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

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

Worked solutions can be found here: Integration problem solutions