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_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -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.
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
`int_0^2 e^x dx` = ______.
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
`int_-9^9 x^3/(4 - x^2)` dx = ______
`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` dx = ?
`int_0^1 x tan^-1x dx` = ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
Which of the following is true?
`int_0^1 "e"^(5logx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Show that `int_0^(pi/2) (sin^2x)/(sinx + cosx) = 1/sqrt(2) log (sqrt(2) + 1)`
Evaluate the following:
`int_0^(pi/2) "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)
If `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`, then the value of k is:
`int (dx)/(e^x + e^(-x))` is equal to ______.
`int_(-5)^5 x^7/(x^4 + 10) 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 ______.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
Solve the following.
`int_1^3 x^2 logx dx`
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Evaluate the following integral:
`int_-9^9 x^3 / (4 - x^2) dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
