Integrate 2x cos⁡(x^2+3).

Category: QuestionsIntegrate 2x cos⁡(x^2+3).
Editor">Editor Staff asked 11 months ago

Integrate 2x cos⁡(x^2+3).
 
(a) sin⁡(x^2+3)+C
 
(b) sin^2⁡(x^2+3)+C
 
(c) cot⁡(x^2+3)+C
 
(d) -sin⁡(x^2+3)+C
 
I got this question during a job interview.
 
Question is taken from Methods of Integration-2 in section Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct choice is (a) sin⁡(x^2+3)+C
 
To explain: ∫ 2x cos⁡(x^2+3) dx
 
Let x^2+3=t
 
Differentiating w.r.t x, we get
 
2x dx=dt
 
∫ 2x cos⁡(x^2+3) dx=∫ cos⁡t dt
 
=sin⁡t+C
 
Replacing w.r.t x, we get
 
∴∫ 2x cos⁡(x^2+3) dx=sin⁡(x^2+3)+C