Advertisements
Advertisements
प्रश्न
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Advertisements
उत्तर
We have I = `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
= `int_0^(pi/4) sqrt((sinx + cosx)^2) "d"x`
= `int_0^(pi/4) (sinx + cosx) "d"x`
= `(-cosx + sinx)_0^(pi/4)`
I = 1.
APPEARS IN
संबंधित प्रश्न
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)dx`
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
Prove that `int_0^af(x)dx=int_0^af(a-x) dx`
hence evaluate `int_0^(pi/2)sinx/(sinx+cosx) dx`
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Evaluate`int (1)/(x(3+log x))dx`
Evaluate : ∫ log (1 + x2) dx
Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
`int_0^{pi/2} xsinx dx` = ______
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_{pi/6}^{pi/3} sin^2x dx` = ______
`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______
Which of the following is true?
Show that `int_0^(pi/2) (sin^2x)/(sinx + cosx) = 1/sqrt(2) log (sqrt(2) + 1)`
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:
Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - x)dx`
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
`int_0^(π/2)((root(n)(secx))/(root(n)(secx + root(n)("cosec" x))))dx` is equal to ______.
`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.
Evaluate `int_-1^1 |x^4 - x|dx`.
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 the following integral:
`int_-9^9 x^3/(4-x^2)dx`
Evaluate:
`int_0^6 |x + 3|dx`
Which property is useful for piecewise functions or modulus (absolute value) functions?
Which expression equals \[\int_{a}^{b} f(x)\,dx\] by \[P_3\] : The "King's Rule"?
When is \[P_4\] : Special Case of \[P_3\] applied?
