Advertisements
Advertisements
प्रश्न
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
विकल्प
4
2
1
0
Advertisements
उत्तर
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is 4.
Explanation:
`int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`
Taking LHS = `int_0^(2π) cos^2 x dx`
= `2int_0^π cos^2 x dx` ...[∵ cos2 x is an even function]
= `2 xx 2int_0^(π/2) cos^2 x dx` ...[∵ cos2 x is an even function]
= `4int_0^(π/2) cos^2 x dx`
On comparing both sides, we get
k = 4.
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| 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.
Evaluate : ∫ log (1 + x2) dx
Choose the correct alternative:
`int_(-9)^9 x^3/(4 - x^2) "d"x` =
`int_2^4 x/(x^2 + 1) "d"x` = ______
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
`int_0^{pi/2} log(tanx)dx` = ______
Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` is equal to
`int_0^1 1/(2x + 5) dx` = ______.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.
`int_0^(pi/4) (sec^2x)/((1 + tanx)(2 + tanx))dx` equals ______.
`int_0^(π/4) x. sec^2 x dx` = ______.
Evaluate `int_-1^1 |x^4 - x|dx`.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following integral:
`int_-9^9 x^3/(4-x^2)dx`
Solve.
`int_0^1e^(x^2)x^3dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
Evaluate:
`int_0^6 |x + 3|dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/(9x^2 - 1) dx`
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
