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Definite Integration question

2021 · Shift 2 · Q30

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2021 · Shift 2 · Q30

Definite Integration question

2021 · Shift 2 · Q30

JEE AdvancedMathematicsDefinite IntegrationNumerical+2 / −1

Let

{g_i}:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R,i = 1,2

, and

f:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R

be functions such that

{g_1}(x) = 1,{g_2}(x) = |4x - \pi |

and

f(x) = {\sin ^2}x

, for all

x \in \left[ {{\pi \over 8},{{3\pi } \over 8}} \right]

. Define

{S_i} = \int\limits_{{\pi \over 8}}^{{{3\pi } \over 8}} {f(x).{g_i}(x)dx}

, i = 1, 2 The value of

{{16{S_1}} \over \pi }

is

\underline{\hspace{2cm}}

.

Numerical answer

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