Advertisements
Advertisements
प्रश्न
Evaluate: `intsinsqrtx/sqrtxdx`
उत्तर
`Let I=int(sinsqrtx/sqrtx)dx`
`Let sqrtx=t`
`1/(sqrtx)=dt/dx`
`1/sqrtxdx=2dt`
`therefore I=2intsintdt`
`=-2cost+C`
`=-2cos(sqrtx)+C`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
`int 1/(1 + cos x)` dx = _____
A) `tan(x/2) + c`
B) `2 tan (x/2) + c`
C) -`cot (x/2) + c`
D) -2 `cot (x/2)` + c
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
(i) \[\int x^4 dx\]
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate:
Evaluate the following definite integral:
Evaluate the following integral:
\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is