Find ∫7 cos⁡mx dx.

Category: QuestionsFind ∫7 cos⁡mx dx.
Editor">Editor Staff asked 11 months ago

Find ∫7 cos⁡mx dx.
 
(a)
7sinmx
x
+C
 
 
(b)
7sinmx
m
+C
 
 
(c)
sinmx
x
+C
 
 
(d)
sinx
m
+C
 
 
I got this question in an interview for job.
 
This is a very interesting question from Methods of Integration-1 in chapter 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

The correct answer is (b)
7sinmx
m
+C
 
 
Easy explanation: Using Integration by Substitution, Let xm=t
 
Differentiating w.r.t x, we get
 
mdx=dt
 

∫7cosmxdx=∫
(7cost)
m
dt
 
 
=
7
m
∫costdt=
7
m
(sint)+C
 
 
Replacing t with mx again we get,
 
∫7cosmxdx=
7sinmx
m
+C