Mathematics

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

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

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### 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. $\dfrac{1}{3}(\sqrt{32}-\sqrt{27})$

1 Verified Answer | Published on 17th 09, 2020

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. $\dfrac{\pi^2}{4}$

1 Verified Answer | Published on 17th 09, 2020

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. $-9$

1 Verified Answer | Published on 17th 09, 2020

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. $\displaystyle \frac{\pi a^{2}}{4}$

If $y=2^23^{2x}5^{-5}7^{-5}$ then $\dfrac{dy}{dx}=$