Integration

1

The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x2 ≤ 4y and y ≤ 1 + √x } is

  1. 59/12
  2. 3/2
  3. 7/3
  4. 5/2
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2

The integral 0π √(1 + 4 sin2x/2 - 4 sinx/2) dx equals

  1. 4√3 - 4
  2. 4√3 - 4 - π/3
  3. 2π/3 - 4 - 4√3
  4. π - 4
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3

The integral ∫(1 + x - 1/x)ex + 1/x dx  is equal to

  1. xex + 1/x + c
  2. (x + 1)ex + 1/x + c
  3. (x - 1)ex + 1/x + c
  4. -xex + 1/x + c
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4

If the integral ∫ (5 tan x / tan x − 2)dx = x + a ln |sin x - 2 cos x| + k, then a is equal to

  1. -1
  2. 2
  3. -2
  4. 1
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5

If g(x) = 0x cos4t dt, then g(x + π) equals

  1. g(x) - g(π)
  2. g(x) / g(π)
  3. g(x) + g(π)
  4. g(x).g(π)
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6

0π [cot x] dx, where [.] denotes the greatest integer function, is equal to

  1. -π/2
  2. 1
  3. -1
  4. π/2
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7

010π |sin x| dx is

  1. 8
  2. 10
  3. 18
  4. 20
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8

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is

  1. 3
  2. 6
  3. 9
  4. 12
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9

The integral \( \int \dfrac{2x^{12}+5x^9}{(x^5+x^3+1)^3} dx \) is equal to:

  1. \( \dfrac{-x^5}{(x^5+x^3+1)^2} + C \)
  2. \( \dfrac{x^{10}}{2(x^5+x^3+1)^2} + C \)
  3. \( \dfrac{x^5}{2(x^5+x^3+1)^2} + C \)
  4. \( \dfrac{-x^{10}}{2(x^5+x^3+1)^2} + C \)
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