Mathematics

# For $n\in N$, $0 < t < \pi/2$; the value of $\displaystyle\int^{n\pi +t}_0(|\cos x|+|\sin x|)dx=$?

$2n-\sin t-\cos t-1$

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

#### Realted Questions

Q1 Subjective Hard
$\displaystyle\int \dfrac{7x-4}{(x-1)^2(x+2)}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Multiple Correct Hard
$\displaystyle \int \frac{\left \{ f\left ( x \right ).{\phi}' \left ( x \right )-{f}' \left ( x \right ).\phi \left ( x \right ) \right \}}{f\left ( x \right ).\phi \left ( x \right )}\left \{ \log \phi \left ( x \right )-\log f\left ( x \right ) \right \}dx$ is equal to
• A. $\displaystyle \log \frac{\phi \left ( x \right )}{f\left ( x \right )}k$
• B. $none\ of\ these$
• C. $\displaystyle \frac{1}{2}\left \{ \log \frac{\phi \left ( x \right )}{f\left ( x \right )} \right \}^{2}+k$
• D. $\displaystyle \frac{\phi \left ( x \right )}{f\left ( x \right )}log\frac{\phi \left ( x \right )}{f\left ( x \right )}+k$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle\int \dfrac{(7)^{x^{\dfrac{1}{2}}}}{x^3}dx=k(7)^{x^{\dfrac{1}{2}}}+c$ then k$=$ ___________.
• A. $\dfrac{-1}{7log_e 7}$
• B. $\dfrac{1}{7}$
• C. $\dfrac{1}{log_e7}$
• D. $\dfrac{-1}{2log_e 7}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\displaystyle\int\frac{xe^x}{(x+1)^2}dx.$

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