Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int \sqrt{9 - x^2} \text{ dx}\]
\[ = \int \sqrt{3^2 - x^2} \text{ dx}\]
\[ = \frac{x}{2}\sqrt{3^2 - x^2} + \frac{3^2}{2} \sin^{- 1} \left( \frac{x}{3} \right) + C \left[ \because \int\sqrt{a^2 - x^2} \text{ dx } = \frac{1}{2}x\sqrt{a^2 - x^2} + \frac{1}{2} a^2 \text{ sin}^{- 1} \left( \frac{x}{a} \right) + C \right]\]
\[ = \frac{x}{2}\sqrt{9 - x^2} + \frac{9}{2} \sin^{- 1} \left( \frac{x}{3} \right) + C\]
APPEARS IN
संबंधित प्रश्न
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
sin (ax + b) cos (ax + b)
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (logx)2.dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int x^2/sqrt(1 - x^6)` dx = ________________
`int logx/x "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate:
`int sqrt((a - x)/x) dx`
`int "cosec"^4x dx` = ______.
Evaluate `int 1/(x(x-1))dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
