Mathematics

# $\int { \left( { e }^{ ln\quad sinx }-cos\quad x \right) }$ dx is equal to :

$sin x-x cosx +c$

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

#### Realted Questions

Q1 Single Correct Medium
If $I_{1}=\displaystyle \int_{e}^{e^{2}}\dfrac{dx}{\ell n x}$ and $I_{2}=\int_{1}^{2} \dfrac{e^{x}}{x}dx$, then
• A. $2I_{1}=I_{2}$
• B. $I_{1}=2I_{2}$
• C. $I_{1}+I_{2}=0$
• D. $I_{1}=I_{2}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

$\displaystyle \int{\sqrt{x-\sqrt{x^{2}-4}}} dx\displaystyle =\left [ \frac{1}{3}\left ( \sqrt{x+2}-\sqrt{x-2} \right )^{3} +2\left ( \sqrt{x+2}+\sqrt{x-2} \right )\right ]+C$

##### REASON

The integral in assertion can be computed by substituting $\displaystyle \left ( \sqrt{x+2}-\sqrt{x-2} \right )^{2}=2t.$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate:
$\int { \sqrt { { x }^{ 2 }-16 } } \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
What is an integrand?
• A. The symbol $dx$
• B. The interval $[a,b]$
• C. None of these
• D. The function $f(x)$ to be integrated

Let $F: R\rightarrow R$ be a thrice differential function. Suppose that $F(1) = 0, F(3) = -4$ and $F'(x)<0$ for all $x\in\left(\dfrac{1}{2},3\right)$. Let $f(x) = xF(x)$ for all $x\in R$.