Advertisements
Advertisements
Question
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.
Options
1
2
3
4
Advertisements
Solution
`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
RELATED QUESTIONS
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
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_0^4 |x - 1| 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.
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` 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 "e"^(3"x")/("e"^(3"x") + 1)` dx
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
Find `dy/dx, if y = cos^-1 ( sin 5x)`
`int_0^2 e^x dx` = ______.
`int_"a"^"b" "f"(x) "d"x` = ______
`int_1^2 1/(2x + 3) dx` = ______
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`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/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^pi x sin^2x dx` = ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2)) dx` is
Evaluate: `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tanx)`
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
`int_a^b f(x)dx` = ______.
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
`int_0^1|3x - 1|dx` equals ______.
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_0^(π//4) log (1 + tanx)dx`.
Evaluate the following integral:
`int_0^1 x(1 - 5)^5`dx
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate: `int_-1^1 x^17.cos^4x dx`
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
