GATE Questions & Answers of Evaluation of definite integrals

What is the Weightage of Evaluation of definite integrals in GATE Exam?

Total 3 Questions have been asked from Evaluation of definite integrals topic of Calculus subject in previous GATE papers. Average marks 2.00.

The solution for $\int\limits_0^{\pi/6}\cos^43\theta\sin^36\theta d\theta$ is:

what is the value of the definite integral $\int\limits_0^\mathrm a\frac{\sqrt{\mathrm x}}{\sqrt{\mathrm x}+\sqrt{\mathrm a-\mathrm x}}dx$

The value of $\int\limits_0^3\int\limits_0^x\left(6-x-y\right)dx\;dy$ is