Integration (Indefinite)

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

Click on each question to see answer & solution.

Question No: #11

If slope of any curve at the point `(x,y)` be `-\frac{x}{y}` and the curve passing through the point `(1,1)`, then find the equation of the curve.
Ans: `x^2 + y^2 = 2`
SEE SOLUTION

Question No: #12

If slope of any curve at the point `(x,y)` be `-y` and the curve passing through the point `(2,1)`, then find the equation of the curve.
Ans: `log|y| = 2-x`
SEE SOLUTION

Question No: #13

If slope of any curve at the point `(x,y)` be `e^x+\frac{1}{1+x^2}` and the curve passing through the point `(0,1)`, then find the equation of the curve.
Ans: `y = e^x + tan^{-1}x`
SEE SOLUTION

Question No: #14

If $f''(x)=\cos^2x+3$, $f'(0)=0=f(0)$, then find `f(x)`.
Ans: `f(x) = \frac{7x^2}{4} - \frac{cos2x}{8} + 1/8`
SEE SOLUTION

Question No: #15

If $f'(x)=x+\frac{1}{x^2}$, `f(3)=4`, then find `f(x)`.
Ans: `f(x) = \frac{x^2}{2} - 1/x - 1/6`
SEE SOLUTION

Question No: #16

`\int \ \frac{1+x+x^2}{x^2(1+x)} \ dx`
Ans: `-\frac{1}{x} + \log |1+x| + c`
SEE SOLUTION

Question No: #17

`\int \ \frac{1+2x^2}{x^2 (1+x^2)} \ dx`
Ans: `-\frac{1}{x} + \tan^{-1}x + c`
SEE SOLUTION

Question No: #18

`\int \ \frac{dx}{\sqrt{ax+b} + \sqrt{ax-b}}`
Ans: `\frac{1}{3ab} {(ax+b)^{\frac{3}{2}} - (ax-b)^{\frac{3}{2}}} + c`
SEE SOLUTION

Question No: #19

`\int \ \frac{\cos 2x + \sin x}{1 + 2 \sin x} \ dx`
Ans: `x + cosx + c`
SEE SOLUTION

Question No: #20

`\int \ \frac{\cos x - \cos 2x}{1 - \cos x} \ dx`
Ans: `x + 2sinx + c`
SEE SOLUTION