IBDP Past Year Exam Questions – Introduction to Integration

1.[M97/P1]

Find the indefinite integral    $\int {\left(x^2–1\right)}^{3}x dx$ .

2.[M97/P1]

Using the substitution  $u=\frac{1}{2}x+1$ , or otherwise, find the integral

                            $\int x\sqrt{\frac{1}{2}x+1} dx$ .

3. [M15/P1/TZ1]

(a)  Find  $\int \left(1+{\tan }^{2}x\right) dx$ .    [2 marks]

(b)   Find   $\int {\sin }^{2}x dx$ .        [3 marks]