Advertisements
Advertisements
प्रश्न
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
Advertisements
उत्तर
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to e – 1.
Explanation:
Let I = `int_0^(pi/2) cos x "e"^(sinx) "d"x`
Put sin x = t
⇒ cos x "d"x` = dt
∴ I = `int_0^1 "e"^"t" "dt"`
= `["e"^"t"]_0^1`
= `"e"^1 - "e"^0`
= e – 1
APPEARS IN
संबंधित प्रश्न
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
Evaluate`int (1)/(x(3+log x))dx`
Evaluate : `int _0^(pi/2) "sin"^ 2 "x" "dx"`
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_1^2 1/(2x + 3) dx` = ______
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
`int_-9^9 x^3/(4 - x^2)` dx = ______
`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.
If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_0^pi x sin^2x dx` = ______
Which of the following is true?
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0
⇒ `1/4 (square - square)` = 0
⇒ b4 – `square` = 0
⇒ (b2 – a2)(`square` + `square`) = 0
⇒ b2 – `square` = 0 as a2 + b2 ≠ 0
⇒ b = ± `square`
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
Evaluate `int_-1^1 |x^4 - x|dx`.
Evaluate the following definite integral:
`int_4^9 1/sqrt"x" "dx"`
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Evaluate:
`int_0^6 |x + 3|dx`
Evaluate the following integral:
`int_0^1x(1-x)^5dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
