Advertisements
Advertisements
प्रश्न
Evaluate : `int_0^(pi/4) sin 4x sin 3x *dx`
उत्तर
`int_0^(pi/4) sin 4x sin 3x *dx`
= `(1)/(2) int_0^(pi/4) 2 sin 4x sin 3x *dx`
= `(1)/(2) int_0^(pi/4) [cos (4x - 3x) - cos(4x + 3x)]*dx`
= `(1)/(2) int_0^(pi/4) cos x*dx - (1)/(2) int^(pi/4)cos 7x*dx`
= `(1)/(2)[sinx]_0^(pi/4) - (1)/(2)[(sin7x)/7]_0^(pi/4)`
= `(1)/(2)[sin pi/4 - sin 0] - (1)/(14)[sin (7pi)/4 - sin 0]`
= `(1)/(2)[1/sqrt(2) - 0] - (1)/(14)[sin (2pi - pi/4) - 0]`
= `(1)/(2sqrt(2)) - (1)/(14)(- sin pi/4)`
= `(1)/(2sqrt(2)) + (1)/(14sqrt(2))`
= `(7 + 1)/(14sqrt(2))`
= `(4)/(7sqrt(2))`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^(pi/4) (cosx)/(4 - sin^2x)*dx`
Evaluate the following : `int_((-pi)/4)^(pi/4) (x + pi/4)/(2 - cos 2x)*dx`
Evaluate the following : `int_((-pi)/4)^(pi/4) x^3 sin^4x*dx`
`int_0^(log5) (e^x sqrt(e^x - 1))/(e^x + 3) * dx` = ______.
Choose the correct option from the given alternatives :
`int_0^9 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx` =
Choose the correct option from the given alternatives :
The value of `int_((-pi)/4)^(pi/4) log((2+ sin theta)/(2 - sin theta))*d theta` is
Evaluate the following : `int_0^1 (cos^-1 x^2)*dx`
Evaluate the following : `int_0^pi x*sinx*cos^4x*dx`
Evaluate the following : `int_0^1 (1/(1 + x^2))sin^-1((2x)/(1 + x^2))*dx`
Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.
Evaluate the following integrals : `int_0^"a" x^2("a" - x)^(3/2)*dx`
State whether the following is True or False : `int_0^"a" f(x)*dx = int_"a"^0 f("a" - x)*dx`
Solve the following : `int_2^3 x/((x + 2)(x + 3))*dx`
Solve the following:
`int_1^3 x^2 log x*dx`
Solve the following : `int_4^9 (1)/sqrt(x)*dx`
Solve the following : `int_3^5 dx/(sqrt(x + 4) + sqrt(x - 2)`
Solve the following : `int_0^1 (1)/(sqrt(1 + x) + sqrt(x))dx`
Solve the following : `int_0^4 (1)/sqrt(x^2 + 2x + 3)*dx`
Solve the following : `int_2^4 x/(x^2 + 1)*dx`
Solve the following : `int_0^1 (1)/(2x - 3)*dx`
`int_1^9 (x + 1)/sqrt(x) "d"x` =
Evaluate `int_0^1 "e"^(x^2)*"x"^3 "d"x`
`int_((-pi)/8)^(pi/8) log ((2 - sin x)/(2 + sin x))` dx = ______.
`int_(-2)^2 sqrt((2 - x)/(2 + x))` = ?
Prove that: `int_0^(2a) f(x)dx = int_0^a f(x)dx + int_0^a f(2a - x)dx`
Evaluate the following definite integrats:
`int_4^9 1/sqrt x dx`
Evaluate the following definite intergrals.
`int_1^3 logx* dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5) dx`
Evaluate:
`int_0^1 |x| dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/((9x^2-1 )`dx
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Solve the following.
`int_1^3 x^2 log x dx `
Evaluate the following definite intergral:
`int_1^3logxdx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5).dx`
Solve the following.
`int_1^3 x^2 log x dx`
Evaluate the following definite integral:
`int_1^3 logx.dx`
Evaluate the following definite intergral:
`int_4^9 1/sqrtx dx`
