todai-math 2021 QI.3

todai-math · Japan · todai-engineering-math__paper1 Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer)

Calculate the following definite integral: $$I = \int_{0}^{\sin\theta} \frac{\arctan(\arcsin x)}{\sqrt{1 - x^{2}}} \mathrm{~d}x$$ where $0 < \theta < \pi/2$.

Calculate the following definite integral:
$$I = \int_{0}^{\sin\theta} \frac{\arctan(\arcsin x)}{\sqrt{1 - x^{2}}} \mathrm{~d}x$$
where $0 < \theta < \pi/2$.

Paper Questions

QI.1 QI.2 QI.3 QII.1 QII.2 QII.3