Advertisements
Advertisements
प्रश्न
Evaluate the following : `int_((-pi)/4)^(pi/4) x^3 sin^4x*dx`
उत्तर
Let I = `int_((-pi)/4)^(pi/4) x^3 sin^4x*dx`
Let f(x) = `x^3 sin^4x`
∴ f( –x) = `(-x)^3 sin^4(- x)`
= `-x^3sin^4x`
= `-f(x)`
∴ f is an odd function.
∴ `int_((-pi)/4)^(pi/4) f(x)*dx = 0, "i.e." int_((-pi)/4)^(pi/4) x^3 sin^4x*dx` = 0.
APPEARS IN
संबंधित प्रश्न
Prove that:
`int 1/(a^2 - x^2) dx = 1/2 a log ((a +x)/(a-x)) + c`
Show that: `int _0^(pi/4) log (1 + tanx) dx = pi/8 log2`
Evaluate : `int_0^(pi/4) sin^4x*dx`
Evaluate : `int_0^1 x tan^-1x*dx`
Evaluate : `int_0^(pi/4) (cosx)/(4 - sin^2x)*dx`
Evaluate the following:
`int_0^(pi/2) log(tanx)dx`
Evaluate the following : `int_0^pi x sin x cos^2x*dx`
Evaluate the following : `int_0^(pi/4) (tan^3x)/(1 +cos2x)*dx`
Evaluate the following : `int_0^(pi/4) (cos2x)/(1 + cos 2x + sin 2x)*dx`
Evaluate the following : `int_0^4 [sqrt(x^2 + 2x + 3]]^-1*dx`
Evaluate the following : if `int_a^a sqrt(x)*dx = 2a int_0^(pi/2) sin^3x*dx`, find the value of `int_a^(a + 1)x*dx`
Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`
Choose the correct alternative :
`int_(-9)^9 x^3/(4 - x^2)*dx` =
Choose the correct alternative :
`int_4^9 dx/sqrt(x)` =
Choose the correct alternative :
`int_2^3 x^4*dx` =
Choose the correct alternative :
`int_"a"^"b" f(x)*dx` =
Choose the correct alternative :
`int_(-7)^7 x^3/(x^2 + 7)*dx` =
Fill in the blank : `int_0^1 dx/(2x + 5)` = _______
Fill in the blank : If `int_0^"a" 3x^2*dx` = 8, then a = _______
Fill in the blank : `int_2^3 x/(x^2 - 1)*dx` = _______
Fill in the blank : `int_(-9)^9 x^3/(4 - x^2)*dx` = _______
`int_0^"a" 4x^3 "d"x` = 81, then a = ______
Evaluate `int_0^1 (x^2 + 3x + 2)/sqrt(x) "d"x`
Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2)) "d"x`
`int_0^(pi/2) (cos x)/((4 + sin x)(3 + sin x))`dx = ?
Evaluate the following definite integrals:
`int _1^2 (3x) / ( (9 x^2 - 1)) * dx`
Evaluate the following definite integrals: `int_-2^3 1/(x + 5) *dx`
Evaluate the following integrals:
`int_0^1 x(1 - x)^5 dx`
Evaluate the following definite integral:
`int_1^3 log x dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x + 5)dx`
Evaluate the following definite intergral:
`int_4^9 1/sqrt(x)dx`
Evaluate the following definite intergral:
`int _1^3logxdx`
Evaluate the following definite intergral:
`int_4^9(1)/sqrtxdx`
Evaluate the following definite intergral:
`int_1^2(3x)/(9x^2-1).dx`
Solve the following.
`int_1^3 x^2 log x dx`
Evaluate the following integral:
`int_-9^9 x^3/(4-x^2) dx`
Solve the following.
`int_0^1e^(x^2) x^3 dx`
Evaluate the following definite intergral.
`int_1^2 (3x)/((9x^2 - 1))dx`
