₀^{π/2} 300 x+100 x/ x+ x d x=

Correct Answer is : 100π100 π100π

Correct Answer is : 100π100 π100π

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MHTCET 26 Apr 2025 Shift 2 Paper

Question : 110 of 150

Marks: +1, -0

\int_{0}^{\frac{\pi}{2}} \frac{300 \sin x+100 \cos x}{\sin x+\cos x} d x=\ldots

Solution:

Concept:

Use the standard result for integrals of the form

\frac{a\sin x+b\cos x}{\sin x+\cos x}

from

0

\frac{\pi}{2}

Explanation:

The given integral is

I = \int_{0}^{\frac{\pi}{2}} \frac{300\sin x+100\cos x}{\sin x+\cos x} dx

For

\int_{0}^{\frac{\pi}{2}} \frac{a\sin x+b\cos x}{\sin x+\cos x} dx = \frac{\pi}{4}(a+b)

, compare the numerator.

Here,

a = 300

and

b = 100

So,

I = \frac{\pi}{4}(300+100)

This gives

I = \frac{\pi}{4} \times 400 = 100\pi

Answer:

100\pi

, which is option A.

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