A-level Mathematics/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:

(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)$\underset{0}{\overset{2}{\int }}x+1dx$

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

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