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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

Consider the integrals I _ 1 = ∫ e^ x2 cos xdx and I _ 2 = ∫ xe^ x2...

Consider the integrals

{I}_{1} = ∫ e^{x2}cos xdx

and

{I}_{2} = ∫ xe^{x2}sin xdx.

Then,

{I}_{1} + 2{I}_{2}

simplifies to (where,

c

is the constant of integration)

Options

A $e^{x}sin x + c$
B $e^{x^{2}}cos x + c$
C $2e^{x^{2}}sin x + c$
D $e^{x^{2}}sin x + c$

Correct answer

D. $e^{x^{2}}sin x + c$

Step-by-step solution

{I}_{1} + 2{I}_{2} = ∫ \left(e^{x^{2}}cos x + 2xe^{x^{2}}sin x\right)dx

= ∫ d\left(e^{x^{2}}sin x\right)

= e^{x^{2}}sin x + c

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