Mathematics

# $\int ^\pi _0 | cos x|^3 dx$ is equal to

$\dfrac{4}{3}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int\frac{dx}{1-\sin^{4}x}=$
• A. $\displaystyle \frac{1}{2} \left[\tan x-\frac{1}{\sqrt{2}}\tan^{-1}(\sqrt{2} \tan x) \right] +c$
• B. $\displaystyle \frac{1}{2} \left[\tan x+\frac{1}{2\sqrt{2}} \cot^{-1}(\sqrt{2} \tan x) \right ] +c$
• C. $\displaystyle \frac{1}{2} \left[ \tan x-\frac{1}{2\sqrt{2}}\cot^{-1}(\sqrt{2} \tan x) \right ] +c$
• D. $\displaystyle \frac{1}{2} \left[\tan x+\frac{1}{\sqrt{2}} \tan^{-1} (\sqrt{2} \tan x) \right] +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int {\dfrac{{2x - 1}}{{2{x^2} + 2x + 1}}} dx =$
• A. $\frac{1}{2}\ln \left| {2{x^2} + 2x + 1} \right| + 2{\tan ^{ - 1}}\left( {2x + 1} \right) + c$
• B. $-\frac{1}{2}\ln \left| {2{x^2} + 2x + 1} \right| - 2{\tan ^{ - 1}}\left( {2x + 1} \right) + c$
• C. $-\frac{1}{2}\ln \left| {2{x^2} + 2x + 1} \right| + 2{\tan ^{ - 1}}\left( {2x + 1} \right) + c$
• D. $\frac{1}{2}\ln \left| {2{x^2} + 2x + 1} \right| - 2{\tan ^{ - 1}}\left( {2x + 1} \right) + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Find $\int (x+3)\sqrt{3-4x-x^2}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium

Evaluate the following definite integral:

$\displaystyle\int_{1}^{2} \dfrac 2x\ dx$

Solve $\displaystyle\int { \dfrac { 1 }{ 3{ x }^{ 2 }+13x+10 } dx }$