(a) Evaluate the following integral: $$\int\limits_{0}^{1} \frac{\log…

Question

(a) Evaluate the following integral:

$$\int\limits_{0}^{1} \frac{\log x \, dx}{\sqrt{1-x^2}}$$

(b) Define beta function and prove that

$$\beta(p,q) = \int\limits_{0}^{\infty} \frac{y^{q-1} \, dy}{(1+y)^{p+q}}$$

Related pages

• Gamma Function — topic
• Engineering Mathematics-I syllabus

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