Advertisements
Advertisements
प्रश्न
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
उत्तर
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an Odd function.
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
By using the properties of the definite integral, evaluate the integral:
`int_0^4 |x - 1| dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_2^3 x/(x^2 - 1)` dx = ______
`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.
`int_0^1 (1 - x)^5`dx = ______.
`int_0^{pi/2} cos^2x dx` = ______
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
Which of the following is true?
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int_0^(pi/2) "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
`int_a^b f(x)dx` = ______.
Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.
Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.
If f(x) = `{{:(x^2",", "where" 0 ≤ x < 1),(sqrt(x)",", "when" 1 ≤ x < 2):}`, then `int_0^2f(x)dx` equals ______.
If `int_0^(π/2) log cos x dx = π/2 log(1/2)`, then `int_0^(π/2) log sec dx` = ______.
Evaluate `int_0^(π//4) log (1 + tanx)dx`.
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Evaluate the following definite integral:
`int_1^3 log x dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Solve.
`int_0^1e^(x^2)x^3dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
