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Definite Integration question

2024 · 31 Jan · Shift 1 · Q55

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PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 31 Jan · Shift 1 · Q55

Definite Integration question

2024 · 31 Jan · Shift 1 · Q55

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

S=(-1, \infty)

and

f: S \rightarrow \mathbb{R}

be defined as

f(x)=\int_{-1}^x\left(e^t-1\right)^{11}(2 t-1)^5(t-2)^7(t-3)^{12}(2 t-10)^{61} d t \text {, }

Let

\mathrm{p}=

Sum of squares of the values of

x

, where

f(x)

attains local maxima on

S

, and

\mathrm{q}=

Sum of the values of

\mathrm{x}

, where

f(x)

attains local minima on

S

. Then, the value of

p^2+2 q

is

\underline{\hspace{2cm}}

.

Numerical answer

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