Flag Integral Calculus> ∫ln(tanx) dx limit is from 0 to pi/4...
question mark

∫ln(tanx) dx
limit is from 0 to pi/4

Lovey , 10 Years ago
Grade 12
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

I = \int_{0}^{\pi /4}ln(1+tanx)dx
I = \int_{0}^{\pi /4}ln(1+tan(\frac{\pi }{4}-x))dx
I = \int_{0}^{\pi /4}ln(1+\frac{tan\frac{\pi }{4}-tanx}{1+tan\frac{\pi }{4}tanx})dx
I = \int_{0}^{\pi /4}ln(1+\frac{1-tanx}{1+tanx})dx
I = \int_{0}^{\pi /4}ln(\frac{2}{1+tanx})dx
I = \int_{0}^{\pi /4}(ln(2)-ln(1+tanx))dx
I = \int_{0}^{\pi /4}ln(2)dx-\int_{0}^{\pi /4}ln(1+tanx)dx
I = \int_{0}^{\pi /4}ln(2)dx-I
2I = \int_{0}^{\pi /4}ln(2)dx
2I = ln(2)[x]_{0}^{\pi /4}
I = \frac{\pi }{8}ln(2)

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments