1.

Integrate 8 tan^3⁡x sec^2⁡x.(a) 2 tan^4⁡x+C(b) 4 cot^4⁡x+C(c) 2 tan^3⁡x+C(d) tan^4⁡x+CThis question was addressed to me in final exam.Query is from Methods of Integration-2 topic in portion Integrals of Mathematics – Class 12

Answer»

Correct option is (a) 2 tan^4⁡x+C

The EXPLANATION: To FIND: \(\int 8 \,tan^3⁡x \,sec^2⁡x \,DX\)

LET tan⁡x=t

sec^2⁡x dx=dt

∴\(\int 8 \,tan^3⁡x \,sec^2⁡x \,dx=\int 8 \,t^3 \,dt=\frac{8t^4}{4}=2t^4\)

REPLACING t with tan⁡x, we get

\(\int 8 tan^3⁡x sec^2⁡x dx=2 tan^4⁡x+C\)


Discussion

No Comment Found

Related InterviewSolutions