(a) Prove that $$\int\limits_{0}^{t} \operatorname{erf}_c(ax) \, dx =…

Question

(a) Prove that

$$\int\limits_{0}^{t} \operatorname{erf}_c(ax) \, dx = t \operatorname{erf}_c(at) - \frac{1}{a\sqrt{\pi}}(e^{-a^2t^2}-1).$$

(b) Evaluate $\iint_{R} xydxdy$ over the region R in the positive quadrant bounded by the circle $x^2 + y^2 = a^2$.

Related pages

• Error Function — topic
• Engineering Mathematics-I syllabus