Mathematics

# Solve:$\displaystyle \int \frac{3x-2}{\sqrt{3\:+\:2x\:-\:x^2}}dx$

$-3\sqrt{-x^2+2x+3}+\arcsin \left(\frac{1}{2}\left(x-1\right)\right)+C$

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

#### Realted Questions

Q1 Subjective Medium
The acceleration of a motorcycle is given by $a_{x}(t) = At - Br^{2}$, where $A = 1.50\ ms^{-2}$ and $B = 0.120\ ms^{-4}$. The motorcycle is at rest at the origin at time $t = 0$.
Find its position and velocity as functions of time.

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

The value $\displaystyle\int_{-4}^{-5}\sin (x^{2}-3)dx+\int_{-2}^{-1}\sin (x^{2}+12x+33)$ is zero.

##### REASON

$\displaystyle\int_{-a}^{a}f(x)dx=0$ if f(x) is an odd function.

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

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate : $\displaystyle \int_{\pi/6}^{\pi/3}{\cfrac{1}{1+\sqrt{\tan{x}}}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\text { Evaluate: } \displaystyle \int_{-\pi / 2}^{\pi / 2} \dfrac{\cos x}{1+e^{x}} \mathrm{d} \mathrm{x}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
If $\displaystyle I = \int \frac {dx}{(1 + x^4)^{1/4}}$, then I equals
• A. $\displaystyle \frac {1}{2} \tan^{-1} \left ( \frac {x}{(1 + x^4)^{1/4}} \right ) + C$
• B. $\displaystyle \frac {1}{4} \log \left | \frac {1 - (1 + x^4)^{1/4}}{1 + (1 + x^4)^{1/4}} \right | + C$
• C. $\displaystyle \frac {1}{2} \tan^{-1} \frac {(1 + x^4)^{1/4}}{x} - \frac {1}{4} \log \left | \frac {1 - (1 + x^4)^{1/4}}{1 + (1 + x^4)^{1/4}} \right | + C$
• D. $\displaystyle \frac {1}{2} \tan^{-1} \frac {(1 + x^4)^{1/4}}{x} - \frac {1}{4} \log \left | \frac {x - (1 + x^4)^{1/4}}{x + (1 + x^4)^{1/4}} \right | + C$