Advertisements
Advertisements
प्रश्न
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.
पर्याय
1
2
3
4
Advertisements
उत्तर
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to 1.
Explanation:
Let I = `int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)`
= `int_((-pi)/4)^(pi/4) "dx"/(2cos^2x)`
= `1/2 int_((-pi)/4)^(pi/4) sec^2x "d"x`
= `1/2 [tan x]_((-pi)/4)^(pi/4)`
= `1/2 [tan pi/4 - tan (- pi/4)]`
= `1/2[1 + 1]`
= `1/2 xx 2`
= 1
APPEARS IN
संबंधित प्रश्न
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-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.
Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`
Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`
The total revenue R = 720 - 3x2 where x is number of items sold. Find x for which total revenue R is increasing.
Evaluate : ∫ log (1 + x2) dx
Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_0^{pi/2} xsinx dx` = ______
`int_0^1 log(1/x - 1) "dx"` = ______.
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
Evaluate:
`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
`int_0^1 1/(2x + 5) dx` = ______.
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 ______.
`int_0^1|3x - 1|dx` equals ______.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
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 ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
If `int_0^(π/2) log cos x dx = π/2 log(1/2)`, then `int_0^(π/2) log sec dx` = ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following definite integral:
`int_1^3 log x dx`
Evaluate the following integrals:
`int_-9^9 x^3/(4 - x^3 ) dx`
Evaluate the following integral:
`int_0^1x(1-x)^5dx`
