(a) Evaluate the following integral: $$\int_0^1 \frac{\log x \, dx}{\…
Previous year question for Engineering Mathematics-I.
Question
(a) Evaluate the following integral:
$$\int_0^1 \frac{\log x \, dx}{\sqrt{1-x^2}}$$
(b) Define beta function and prove that
$$B(p,q) = \int_0^\infty \frac{y^{q-1} \, dy}{(1+y)^{p+q}}$$
(c) Evaluate $\iint_R xy \, dxdy$ over the region $R$ in the positive quadrant bounded by the circle $x^2 + y^2 = a^2$.
- Year: 2022
- Subject: Engineering Mathematics-I
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