A-level Mathematics/OCR/C2/Integration/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) $\int_{0}^{2} x + 1 \,dx$

(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

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