Home > Definite Integration > JEE Main 2022 > DI-Q9
Definite Integration
Beta and Gamma Functions
JEE Main 2022
Grade 12

Question:

$\int_0^1 x(1 - x)^5 \, dx$ equals:
(1) $\frac{1}{42}$
(2) $\frac{1}{30}$
(3) $\frac{1}{36}$
(4) $\frac{1}{56}$

Step-by-Step Solution

Key Concept: Recognise this as a Beta-function integral $B(2, 6) = \int_0^1 x^{2-1}(1-x)^{6-1} \, dx$, or expand $(1-x)^5$ using the binomial theorem and integrate term by term.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)

Master Definite Integration with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free