Advertisements
Advertisements
Question
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Advertisements
Solution
`intsqrt(1 + sin 5x).dx`
= `intsqrt(sin^2 (5x)/2 + cos^2 (5x)/2 + 2sin (5x)/2 cos (5x)/2) dx`
= `intsqrt((cos (5x)/2 + sin (5x)/2)^2) dx`
= `int(cos (5x)/2 + sin (5x)/2) dx`
= `intcos (5x)/2 dx + sin (5x)/2 dx`
= `(sin (5x)/2)/(5/2) - (cos (5x)/2)/(5/2) + "c"`
∴ I = `2/5 (sin (5x)/2-cos (5x)/2) + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
cot x log sin x
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int sqrt(1 + "x"^2) "dx"` =
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
`int cot^2x "d"x`
`int(1 - x)^(-2) dx` = ______.
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int1/(4 + 3cos^2x)dx` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (logx)^2/x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
