Question

Find ∫7 cos⁡mx dx.

(a) \(\frac{7 \,sin⁡mx}{x}+C\)

(b) \(\frac{7 \,sin⁡mx}{m}+C\)

(c) \(\frac{sin⁡mx}{x}+C\)

(d) \(\frac{sin⁡x}{m}+C\)

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

Answer 1

The correct answer is (b) \(\frac{7 \,sin⁡mx}{m}+C\)

Easy explanation: Using Integration by Substitution, Let xm=t

Differentiating w.r.t x, we get

mdx=dt

∴\(\int 7 \,cos⁡mx \,dx=\int \frac{(7 cos⁡t)}{m} dt\)

=\(\frac{7}{m} \int cos⁡t \,dt=\frac{7}{m} (sin⁡t)+C\)

Replacing t with mx again we get,

\(\int 7 \,cos⁡mx \,dx=\frac{7 \,sin⁡mx}{m}+C\)