Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Advertisements
उत्तर
`int sqrt(1 + sin 2x) dx`
= `intsqrt(cos^2x + sin^2x + 2sin x cos x) dx`
= `intsqrt((cos x + sin x)^2)dx`
= `int(cos x + sinx)dx`
= `int cos x dx + int sin x dx`
= sin x – cos x + c.
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Solve:
dy/dx = cos(x + y)
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int (log x)/(log ex)^2` dx = _________
`int(log(logx))/x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int sin^-1 x`dx = ?
`int1/(4 + 3cos^2x)dx` = ______
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(1+x+x^2/(2!))dx`
