Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : sin4x.cos3x
Advertisements
Solution
Let I = `int sin^4x.cos^3x dx`
= `int sin^4x.cos^2x.cos x dx`
= `int sin^4x (1 - sin^2x) cos x dx`
Put sin x = t
∴ cos x dx = dt
∴ I = `int t^4(1 - t^2)dt`
= `int (t^4 - t^6)dt`
= `int t^4 dt - int t^6 dt`
= `t^5/(5) - t^7/(7) + c`
= `(1)/(5)sin^5x - (1)/(7)sin^7 x + c`.
APPEARS IN
RELATED QUESTIONS
Evaluate :`intxlogxdx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int 1/(cos x - sin x)` dx = _______________
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int(log(logx))/x "d"x`
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int 1/(x(x-1)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
