Integrate the following functions with respect to x : 1x+3-x-4

Integrate the following functions with respect to x :

`1/(sqrt(x + 3) - sqrt(x - 4))`

बेरीज

`int 1/(sqrt(x + 3) - sqrt(x - 4)) "d"x`

= `int 1/(sqrt(x + 3) - sqrt(x - 4)) xx (sqrt(x + 3) + sqrt(x - 4))/(sqrt(x + 3) + sqrt(x - 4)) "d"x`

= `int (sqrt(x + 3) + sqrt(x - 4))/((x + 3) - (x - 4)) "d"x`

= `int (sqrt(x + 3) + sqrt(x - 4))/(x + 3 - x + 4) "d"x`

= `int (sqrt(x + 3) + sqrt(x - 4))/7 "d"x`

= `int sqrt(x + 3)/7 "d"x + int sqrt(x - 4)/7 "d"x`

= `1/7 int (x + 3)^(1/2) "d"x + 1/7 int (x - 4)^(1/2) "d"x`

= `1/7 (x + 3)^(1/2 + 1)/(1/2 + 1) + 1/7 (x - 4)^(1/2 + 1)/(1/2 + 1) + "c"`

= `1/7 (x + 3)^(3/2)/(3/2) + 1/7 (x - 4)^(3/2)/(3/2) + "c"`

= `1/7 xx 2/3 (x + 3)^(3/2) + 1/7 xx 2/3 (x - 4)^(3/2) + "c"`

= `2/21 [(x + 3)^(3/2) + (x - 4)^(3/2)] + "c"`

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पाठ 11: Integral Calculus - Exercise 11.5 [पृष्ठ २०२]

पाठ 11 Integral Calculus
Exercise 11.5 | Q 16 | पृष्ठ २०२

Find the volume of solid generated by rotating the area bounded by x²+y² =36 and the lines x = 0, x = 3 about X -axis.

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 :

`(cos 2x)/(sin^2x cos^2x)`

Integrate the following functions with respect to x :

`(sin4x)/sinx`

Integrate the following functions with respect to x :

cos 3x cos 2x

Integrate the following functions with respect to x :

sin² 5x

Integrate the following functions with respect to x :

`x^3/((x - 1)(x - 2))`

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`