Advertisements
Advertisements
Question
Integrate the functions:
sin x ⋅ sin (cos x)
Advertisements
Solution
Let I `= int sin x sin (cos x) dx`
Put cos x = t
= - sin x dx = dt
Hence, I `= - int sin t dt`
= (cos t) + C
= cos (cos x) + C
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x^x (1 + logx) "d"x`
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
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)
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
