Integration (Indefinite)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

If `f(x)=\frac{1-x}{1+x}` then find `\int \ f{f(\frac{1}{x})}\ dx` where `x\ne0`
Ans: `log|x| + c`
SEE SOLUTION

Question No: #2

If ${f}'(x)=x$, `f(1)=-3` then find `f(x)`.
Ans: `f(x) = 1/2 (x^2 - 7)`
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Question No: #3

If `\int \ f(x)\ dx=\phi(x)`, then find `\int \ x^5f(x^3)\ dx`
Ans: `1/3 x^3 \phi(x^3) - \int x^2 \phi(x^3) dx + c`
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Question No: #4

If `\int \ f(x)\ dx=\phi(x)` then which one is true?
(a)`f(x)=\phi(x)`, (b)$\phi'(x)=f(x)$, (c)$f'(x)=\phi(x)$, (d)`f(x)+\phi(x)=`cosntant.
Ans: (b)
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Question No: #5

Is the value of `\frac{d}{dx}[\int \ f(x)\ dx]` and `\int \ \frac{d}{dx}[f(x)]\ dx` are equal? Justify.

Question No: #6

Find the value of `\int \ e^{3\logx}\ dx`
Ans: `\frac{x^4}{4}+c`
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Question No: #7

If `\frac{dy}{dx}=\frac{x^3+1}{x^2(x+1)}`, then express `y` as a function of `x`.
Ans: `y = x - log|x| - 1/x + c`
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Question No: #8

If `\frac{dy}{dx}=3\sqrt{x}-\frac{1}{\sqrt{x}}`, then express `y` as a function of `x`, where it is given that `y=12` when `x=4`
Ans: `y = 2x^{3/2} - 2\sqrt{x}`
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Question No: #9

If slope of any curve at the point `(x,y)` be `2\sin^2px+2^{3x}+\frac{1}{2x}`, then find the equation of the curve.
Ans: `y = x - \frac{sin2px}{2p} + \frac{2^{3x}}{3log2} + 1/2 log|x| + c`
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Question No: #10

If slope of any curve at the point `(x,y)` be `x^2-2` and the curve passing through the point `(3,8)`, then find the equation of the curve.
Ans: `y = \frac{x^3}{3} -2x + 5`
SEE SOLUTION