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

Integration/Problems