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Jee Main 2025Medium JEE math MCQ

Let for $f(x) = 7 \tan^8 x + 7 \tan^6 x - 3 \tan^4 x - 3 \tan^2 x$, $I_1 = \int_{0}^{\pi/4} f(x) \, dx$ and $I_2 = \int_{0}^{\pi/4} x f(x) \, dx$. Then $7I_1 + 12I_2$ is equal to
  1. A. 2
  2. B. 1
  3. C. $2\pi$
  4. D. $\pi$

Solution

The correct option is **B**. (B. 1)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let for f(x)=7tan8x+7tan6x3tan4x3tan2xf(x) = 7 \tan^8 x + 7 \tan^6 x - 3 \tan^4 x - 3 \tan^2 x, I1=0π/4f(x)dxI_1 = \int_{0}^{\pi/4} f(x) \, dx and I2=0π/4xf(x)dxI_2 = \int_{0}^{\pi/4} x f(x) \, dx. Then 7I1+12I27I_1 + 12I_2 is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep