Advertisements
Advertisements
प्रश्न
`int_1^2 ("e"^(1/x))/(x^2) "d"x` =
विकल्प
`2sqrt("e")(1 + sqrt("e"))`
`sqrt("e")(1 - sqrt("e"))`
`sqrt("e")(sqrt("e") - 1)`
`sqrt("e")(1 + sqrt("e"))`
उत्तर
`sqrt("e")(sqrt("e") - 1)`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_(-4)^2 (1)/(x^2 + 4x + 13)*dx`
Evaluate:
`int_0^(pi/2) sqrt(cos x) sin^3x * dx`
Evaluate : `int_0^(pi/2) (sinx - cosx)/(1 + sinx cosx)*dx`
Evaluate the following : `int_(-1)^(1) (x^3 + 2)/sqrt(x^2 + 4)*dx`
Choose the correct option from the given alternatives :
`int_0^(pi/2) sn^6x cos^2x*dx` =
Choose the correct option from the given alternatives :
If `dx/(sqrt(1 + x) - sqrt(x)) = k/(3)`, then k is equal to
Evaluate the following : `int_(-1)^(1) (1 + x^3)/(9 - x^2)*dx`
Evaluate the following:
`int_0^pi x/(1 + sin^2x) * dx`
Evaluate the following : `int_0^1 sin^-1 ((2x)/(1 + x^2))*dx`
Evaluate the following : If `int_0^k 1/(2 + 8x^2)*dx = pi/(16)`, find k
Evaluate the following : If f(x) = a + bx + cx2, show that `int_0^1 f(x)*dx = (1/(6)[f(0) + 4f(1/2) + f(1)]`
Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`
Evaluate the following integrals:
`int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`
Choose the correct alternative :
If `int_0^"a" 3x^2*dx` = 8, then a = ?
Choose the correct alternative :
`int_0^2 e^x*dx` =
State whether the following is True or False : `int_4^7 ((11 - x)^2)/((11 - x)^2 + x^2)*dx = (3)/(2)`
Solve the following : `int_0^4 (1)/sqrt(x^2 + 2x + 3)*dx`
`int_0^1 sqrt((1 - x)/(1 + x)) "d"x` =
Choose the correct alternative:
`int_0^"a" 3x^5 "d"x` = 8, then a =
State whether the following statement is True or False:
`int_2^3 x/(x^2 + 1) "d"x = 1/2 log 2`
If `int_1^"a" (3x^2 + 2x + 1) "d"x` = 11, find the real value of a
Evaluate:
`int_1^2 1/(x^2 + 6x + 5) dx`
Evaluate `int_1^2 (3x)/((9x^2 - 1)) "d"x`
By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Solution: Let I = `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`
∴ x + 3 = A(x + 2) + B.x
∴ A = `square`, B = `square`
∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`
∴ I = `[square log x + square log(x + 2)]_1^2`
∴ I = `square`
`int_(-5)^5 log ((7 - x)/(7 + x))`dx = ?
Evaluate the following definite integrals: `int_-2^3 1/(x + 5) *dx`
Solve the following `int_1^3 x^2log x dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x + 5)dx`
`int_0^1 1/(2x + 5)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`
`int_a^b f(x) dx = int_a^b f (t) dt`
Evaluate the following definite intergral:
`int_1^2(3x)/((9x^2-1))dx`
Evaluate the following definite intergral:
`int_1^3logxdx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5)dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/ ((9x^2 -1)) dx`
Evaluate the following definite intergral:
`int_1^3 log x·dx`
Evaluate the following definite intergral.
`int_1^2 (3x)/((9x^2 - 1))dx`
Evaluate the following definite intergral:
`int_(-2)^3 1/(x + 5)dx`