Find \int_0^{π/4} \,2 \,tanx \,dx.

(a) log2

(b) log\sqrt{2}

(c) 2 log2

(d) 0

The question was asked during an online interview.

Query is from Fundamental Theorem of Calculus-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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The correct choice is (a) log2

To explain: I=\int_0^{π/4} \,2 \,tanx \,dx

F(x)=∫ 2 tanx dx

=2∫ tanx dx

=2 log|secx|

Therefore, by using the fundamental theorem of calculus, we get

I=F(π/4)-F(0)

=2\left(log|sec \frac{π}{4}|-log|sec0|\right)=2 log\sqrt{2}-log1

=2 log\sqrt{2}=log(\sqrt{2})^2=log2

I=\frac{8}{3} log2-\frac{8}{3}-0+\frac{1}{3}=\frac{8}{3} log2-\frac{7}{3}.