Advertisements
Advertisements
Question
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Solution
`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x`
Put a2 + b2 sin2x = u
(0 + b2 × 2 sin x cos x) dx = du
b2 sin 2x dx = du
sin 2x dx = `1/"b"^2 "du"`
`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x = int (1/"b"^2 "du")/"u"`
= `1/"b"^2 log|"u"| + "c"`
`int (sin 2x)/("a"^2 + "b"^2 sin^2x) "d"x = 1/"b"^2 log|"a"^2 + "b"^2 sin^2 x| + "c"`
APPEARS IN
RELATED QUESTIONS
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
