If - e x -cos x ln x -1- x 2- dx -3-2- then possible value of - can beA- 1B- 2C- 3D- 4

The correct options are A 1 B 2 C 3 D 4∫_ α^α [e^x+(cos x)ln(x+√(1+x^2)) ]dx ⇒∫_ α^α e^x dx {Using odd function property for ∫_ α^α (cos x)ln(x+√(1+x^2)) dx} ...

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Byju's Answer

Standard XII

Mathematics

Rolle's Theorem

If ∫-αα[ e x ...

Question

If $\int_{- α}^{α} [e^{x} + (c o s x) l n (x + \sqrt{1 + x^{2}})] d x > \frac{3}{2}$ , then possible value of $α$ can be

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Solution

The correct options are
A 1
B 2
C 3
D 4
$\int_{- α}^{α} [e^{x} + (c o s x) l n (x + \sqrt{1 + x^{2}})] d x$

$\Rightarrow \int_{- α}^{α} e^{x} d x {Using odd function property for \int_{- α}^{α} (c o s x) l n (x + \sqrt{1 + x^{2}}) d x}$

$\Rightarrow (e^{α} - e^{- α}) > \frac{3}{2}$

$\Rightarrow e^{α} > 2$

$∴ α$ can be 1, 2, 3 or 4.

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