Advertisements
Advertisements
प्रश्न
Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`
Advertisements
उत्तर
Let I = `int_-2^1 sqrt(5 - 4x - x^2)dx`
= `int_-2^1 sqrt(-(x^2 + 4x - 5))dx`
= `int_2^1 sqrt(-(x^2 + 4x + 2^2 - 2^2 - 5))dx`
= `int_-2^1 sqrt(-{(x + 2)^2 - 9})dx`
= `int_-2^1 sqrt(3^2 - (x + 2)^2)dx`
= `[(x + 2)/2 sqrt(3^2 - (x + 2)^2) + 3^2/2 sin^-1 ((x + 2)/3)]_-2^1`
= `0 + 9/2 . π/2 - (0 + 0)`
= `(9π)/4`
संबंधित प्रश्न
Find : `int x^2/(x^4+x^2-2) dx`
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x : `(2x)/(4 - 3x - x^2)`
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
`int sqrt(4^x(4^x + 4)) "d"x`
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
`int x/((x - 1)^2 (x + 2)) "d"x`
`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5) "dt"`
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
If `int dx/sqrt(16 - 9x^2)` = A sin–1 (Bx) + C then A + B = ______.
Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
Integration by partial fractions is a method used to integrate which functions?
Which partial form is appropriate for \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})^{2}(x-\mathrm{b})}\]?
Which factorisation is correct for \[x^{2}-5x+6\]?
