Advertisements
Advertisements
प्रश्न
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
Advertisements
उत्तर
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an Odd function.
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`
Show that `int_0^a f(x)g (x)dx = 2 int_0^a f(x) dx` if f and g are defined as f(x) = f(a-x) and g(x) + g(a-x) = 4.
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
The total revenue R = 720 - 3x2 where x is number of items sold. Find x for which total revenue R is increasing.
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
Choose the correct alternative:
`int_(-9)^9 x^3/(4 - x^2) "d"x` =
`int_2^4 x/(x^2 + 1) "d"x` = ______
Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x)) "d"x`
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______
Evaluate `int_(-1)^2 "f"(x) "d"x`, where f(x) = |x + 1| + |x| + |x – 1|
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – 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)
The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2)) dx` is
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
Let f be a real valued continuous function on [0, 1] and f(x) = `x + int_0^1 (x - t)f(t)dt`. Then, which of the following points (x, y) lies on the curve y = f(x)?
The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.
The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.
If `lim_("n"→∞)(int_(1/("n"+1))^(1/"n") tan^-1("n"x)"d"x)/(int_(1/("n"+1))^(1/"n") sin^-1("n"x)"d"x) = "p"/"q"`, (where p and q are coprime), then (p + q) is ______.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______
`int_0^(2a)f(x)/(f(x)+f(2a-x)) dx` = ______
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
Evaluate `int_1^2(x+3)/(x(x+2)) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following integrals:
`int_-9^9 x^3/(4 - x^3 ) dx`
Evaluate the following integral:
`int_-9^9 x^3/(4-x^2)dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
