Mathematics

Solve:
$$\displaystyle \int_{0}^{\dfrac {\pi}{4}} \tan x\ dx$$.


SOLUTION
$$\log \sec x ]_0^{\dfrac {\pi}{4}}=\log \sec \dfrac {\pi}{4}-\log (sec0)$$
$$=\log \sqrt 2 -\log 1$$
$$=\log \sqrt 2$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
If $$I_1 = \displaystyle \int^{2\pi /3}_{\pi / 2}\left|cos\dfrac{x}{2}cosx\right|dx,I_2=\left|\displaystyle \int_{\pi/2}^{2\pi/3} cos\dfrac{x}{2}cosxdx\right|$$ then $$I_1 - I_2$$ equals 
  • A. $$\dfrac{1}{3}(\sqrt{32}-\sqrt{25})$$
  • B. $$\dfrac{1}{3}(\sqrt{27}-\sqrt{25})$$
  • C. None
  • D. $$\dfrac{1}{3}(\sqrt{32}-\sqrt{27})$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
The value of $$\int^\pi_0 \dfrac{x tan x}{ secx + cos x} dx$$ is
  • A. $$\dfrac{\pi^2}{2}$$
  • B. $$\dfrac{3\pi^2}{2}$$
  • C. $$\dfrac{\pi^2}{3}$$
  • D. $$\dfrac{\pi^2}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Multiple Correct Medium
For $$a\in  R,|a|>1$$, let 
$$\displaystyle \lim_{n\rightarrow \infty}\dfrac{1+\sqrt[3]{2}+........+\sqrt[3]{n}}{n^{7/3}\left(\dfrac{1}{(na+1)^2}+\dfrac{1}{(na+2)^2}+.......+\dfrac{1}{(na+n)^2}\right)}=54$$. Then possible value (s) a is/are
  • A. $$7$$
  • B. $$-6$$
  • C. $$8$$
  • D. $$-9$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Evaluate the integral
$$\displaystyle \int_{0}^{a}\sqrt{a^{2}-x^{2}}dx$$
  • A. $$\displaystyle \frac{a^{2}}{4}$$
  • B. $$\pi {a}^{2}$$
  • C. $$\displaystyle \frac{\pi a^{2}}{2}$$
  • D. $$\displaystyle \frac{\pi a^{2}}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
If $$y=2^23^{2x}5^{-5}7^{-5}$$ then $$\dfrac{dy}{dx}=$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer