The integral ∫012sin-1x2xdx equals from Mathematic

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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51.

The integral 012sin-1x2xdx equals

  • 0π6xdxtanx

  • 0π62tanxdx

  • 0π22xdxtanx

  • 0π62xsinxdx


B.

0π62tanxdx

z = 012sin-1x2xdxPut sin-1x2 = t    x = 2sint  dx = 2costdtAlso, x = 0  t = 0         x = 1  t = π6 I = 0π62t2sint . 2cost dt       = 0π62ttantdt = 0π62xtanxdx


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52.

The area of the plane region bounded by the curve x = y- 2 and the· line y = - x is (in square units)

  • 133

  • 25

  • 92

  • 52


53.

If 0af2a - xdx = m and 0afxdx = n, then 02afxdx is equal to

  • 2m + n

  • m + 2n

  • m - n

  • m + n


54.

- 100100fxdx is equal to

  • - 100100fx2dx

  • - 100100f- x2dx

  • - 100100f1xdx

  • - 100100f- xdx


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55.

- 11ex3 + e- x3ex - e- xdx is equal to

  • e22 - 2e

  • e2 - 2e

  • 2(e2 - e)

  • 0


56.

The family of curves y = easin(x), where a is anarbitrary constant, is represented by thedifferential equation 

  • logy = tanxdydx

  • ylogy = tanxdydx

  • ylogy = sinxdydx

  • logy = cosxdydx


57.

The integrating factor of x dydx + 1 + x y = x is

  • x

  • 2x

  • exlog(x)

  • xex


58.

The solution of the differential equation dydx + 1 = ex + y is

  • x + ex + y = c

  • x - ex + y = c

  • x + e- (x + y) = c

  • x - e- (x + y) = c


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59.

The degree and order of the differential equation y = px + a2p2 + b23, where p = dydx, are respectively.

  • 3, 1

  • 1, 3

  • 1, 1

  • 3, 3


60.

If the distance between (2, 3) and (- 5, 2) is equal to the distance between (x, 2) and (1, 3), then the values of x are

  • - 6, 8

  • 6, 8

  • - 8, 6

  • - 7, 7


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