Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : sin4x.cos3x
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate: `int log ("x"^2 + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int x/(x + 2) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int(1 - x)^(-2) dx` = ______.
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
`int "cosec"^4x dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
