Calculate the area enclosed between the curves $y = x^{2}$ and $y = 2 x - x^{2}$ .

Practise more Integration and Definite Areas Between Curves.

Free questions with an explanation for every one, and full timed Scottish Highers mock tests.

Find $\int (4 cos (2 x) + 3 sin (3 x)) d x$ .
Evaluate the definite integral $\int_{1}^{2} (6 x^{2} - \frac{4}{x ^{2}}) d x$ .
Find the area of the region bounded by the parabola $y = 8 - 2 x^{2}$ and the $x$ -axis.
Given that $\frac{d y}{d x} = 4 x^{3} - 6 x$ and the curve passes through the point $(2, 5)$ , find the equation of the curve.
Evaluate $\int_{0}^{a} (2 x - 3) d x = 4$ , where $a > 0$ . Find the exact value of $a$ .