Mathematics

The integral $${\int}_{\pi/12}^{\pi/4}\dfrac{8\cos 2x}{\left(\tan x+\cot x\right)^{3}}dx$$ equals:


ANSWER

$$\dfrac{15}{128}$$


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 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Solve:
$$\displaystyle \int \cfrac{x^{3}}{1+x^{4}} d x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Solve $$\displaystyle\int\dfrac {\sin x}{(1+\cos x)^{2}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int \dfrac {3^{x}}{\sqrt {1 - 9^{x}}} dx$$ is equal to
  • A. $$(\log 3) \sin^{-1} (3^{x}) + C$$
  • B. $$\dfrac {1}{3}\sin^{-1} (3^{x}) + C$$
  • C. $$\dfrac {1}{9}\sin^{-1} (3^{x}) + C$$
  • D. $$\sin^{-1} (3^{x}) + C$$
  • E. $$\left (\dfrac {1}{\log 3}\right ) \sin^{-1}(3^{x}) + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Find $$\displaystyle \int \sqrt{10 - 4x + 4x^2} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Hard
Let us consider the integral of the following forms
$$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$$
Case I If $$m>0$$, then put $$\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$$
Case II If $$p>0$$, then put $$\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$$
Case III If quadratic equation $$mx^2+nx+p=0$$ has real roots $$\alpha$$ and $$\beta$$, then put $$\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer