If I 1-0-2 x sin x d x - I 2-0-2 x cos x dx- then which of the following is true-A- I1-I2B- I1-2 I2C- I1-I2-0D- I1-I2-2

The correct option is D I_1=∫_0^π/2x cos x dx =∫_0^π/2(π/2 x ) =∫_0^π/2π/2sin x dx I_2 ∴ I_1+I_2=π/2 ...

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Byju's Answer

Standard XII

Mathematics

Equation of Normal at a Point (x,y) in Terms of f'(x)

If I 1=∫0π/2 ...

Question

If $I_{1} = \int_{0}^{\frac{π}{2}} x s i n x d x & I_{2} = \int_{0}^{\frac{π}{2}} x c o s x d x$ , then which of the following is true?

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Solution

The correct option is D

$I_{1} = \int_{0}^{\frac{π}{2}} x c o s x d x = \int_{0}^{\frac{π}{2}} (\frac{π}{2} - x) = \int_{0}^{\frac{π}{2}} \frac{π}{2} s i n x d x - I_{2} ∴ I_{1} + I_{2} = \frac{π}{2}$

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Q. Suppose

I_{1} = \int_{0}^{\frac{π}{2}} c o s (π s i n^{2} x) d x, I_{2} = \int_{0}^{\frac{π}{2}} c o s (2 π s i n^{2} x) d x a n d I_{3} = \int_{0}^{\frac{π}{2}} c o s (π s i n x) d x,

then

Let $I_{1} = {(\frac{π}{4})}^{2} + \sqrt{2}, I_{2} = {(t a n^{- 1} (\frac{1}{e}))}^{2} + \frac{2 e}{\sqrt{e^{2} + 1}}, I_{3} = (t a n^{- 1} e)^{2} + \frac{2}{\sqrt{e^{2} + 1}}$ , then which of the following is true?

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If I1=∫π20x sin x dx &I2=∫π20x cos x dx, then which of the following is true?

The correct option is D I1=∫π20x cos x dx=∫π20(π2−x)=∫π20π2sin x dx −I2∴I1+I2=π2

If $I_{1} = \int_{0}^{\frac{π}{2}} x s i n x d x & I_{2} = \int_{0}^{\frac{π}{2}} x c o s x d x$ , then which of the following is true?

The correct option is D

$I_{1} = \int_{0}^{\frac{π}{2}} x c o s x d x = \int_{0}^{\frac{π}{2}} (\frac{π}{2} - x) = \int_{0}^{\frac{π}{2}} \frac{π}{2} s i n x d x - I_{2} ∴ I_{1} + I_{2} = \frac{π}{2}$