Mathematics

# Let $I={\int}_{0}^{1}\dfrac{\sin x}{\sqrt{x}}dx$ and $J={\int}_{0}^{1}\dfrac{\cos x}{\sqrt{x}}dx$. Then, which one of the following is true?

$I>\dfrac{2}{3}$ and $J>2$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate:
$\displaystyle \int \dfrac{x^2\tan^{-1}(x^3)}{1+x^6}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int x . \cos^{3}{x^{2}} . \sin{x^{2}}dx=$
• A. $\displaystyle \frac{1}{8}\sin^{4}{x^{2}} + c$
• B. $\displaystyle \frac{1}{8}\cos^{4}{x^{2}} + c$
• C. $\displaystyle - \frac{1}{8}\sin^{4}{x^{2}} + c$
• D. $\displaystyle - \frac{1}{8}\cos^{4}{x^{2}} + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate:$\displaystyle \int \sqrt{\frac{a-x}{a+x}}dx$
• A. $\displaystyle \ \sin^{-1} \dfrac{x}{a}+\sqrt{a^{2}-x^{2}}+C$
• B. $\displaystyle \dfrac ax \ \sin^{-1} \dfrac{x}{a}+\sqrt{a^{2}-x^{2}}+C$
• C. none of these
• D. $\displaystyle a \ \sin^{-1} \dfrac{x}{a}+\sqrt{a^{2}-x^{2}}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

Solve $\int {\dfrac{{{x^5}}}{{\sqrt {1 + {x^2}} }}} \,dx$

• A. $\dfrac{1}{{15}}\sqrt {1 + {x^2}} \left( {3{x^4} + 4{x^2} + 8} \right) + C$
• B. $\sqrt {1 + {x^2}} \left( {3{x^4} + 4{x^2} + 8} \right) + C$
• C. None of these
• D. $\dfrac{1}{{15}}\sqrt {1 + {x^2}} \left( {3{x^4} - 4{x^2} + 8} \right) + C$

Consider the integrals $I_1=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{tan x}}$ and $I_2=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sqrt{sin x}dx}{\sqrt{sin }x+\sqrt{cos}x}$