Exams › JEE Main › Maths
Consider the following statements: Statement-1: \(\displaystyle \int_{0}^{\pi/2} \frac{(\sin x)^{5/2}}{(\sin x)^{5/2}+(\cos x)^{5/2}}\,dx = \frac{\pi}{4}\) Statement-2: The region enclosed by the curves \(y=3x\) and \(y=x^2\) has area \(\frac{9}{2}\) square units.
- Statement-1 is correct, Statement-2 is correct, and Statement-2 correctly explains Statement-1
- Statement-1 is correct, Statement-2 is correct, but Statement-2 does not correctly explain Statement-1
- Statement-1 is incorrect, Statement-2 is correct
- Statement-1 is correct, Statement-2 is incorrect
Correct answer: Statement-1 is correct, Statement-2 is correct, but Statement-2 does not correctly explain Statement-1
Solution
Statement-1 is correct as it evaluates to /4 of the integral of a symmetric function over the interval, while Statement-2 is also correct as the area between the curves can be calculated accurately. However, the area of the region defined by Statement-2 does not provide any reasoning or insight into the evaluation of the integral in Statement-1.
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