Mathematics

Evaluate the integral $$\displaystyle \int_{0}^{2\pi} {e}^{ {s} {i} {n}^{2} {n} {x}}$$ .tan(nx).dx $$for $$(n\in N)$$


ANSWER

$$0$$


SOLUTION
$$I=\displaystyle \int_{0}^{2\pi}e^{sin^2 nx}tan (nx)dx$$
$$I=\displaystyle \int_{0}^{2\pi}e^{sin^2}(2n \pi-nx) \cdot tan n (2\pi-x)dx$$
$$=\displaystyle \int_{0}^{2\pi}e^{sin^2 nx}\cdot (-tan  nx)dx$$
$$=-\displaystyle \int_{0}^{2\pi}e^{sin^2 nx}tan  nx   dx$$
$$2I=0$$
$$I=0$$
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
$$\int { x{ e }^{ 2x }dx } = $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Integrate the rational function   $$\cfrac {1}{x(x^n+1)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Prove that:
$$\displaystyle \int_{0}^{1}\cot^{-1}|1-x+x^{2}|dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
 $$\displaystyle \int \cot x {dx}= $$
  • A. $$\ln (\sin^2x) +C$$
  • B. $$ (\sin x) +C$$
  • C. None of these
  • D. $$\ln (\sin x) +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate $$\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer