1
###
The area (in sq. units) of the region

The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x^{2} ≤ 4y and y ≤ 1 + √x } is

- 59/12
- 3/2
- 7/3
- 5/2

2
###
The integral is equal to: #03

The integral _{0}∫^{π} √(1 + 4 sin^{2}x/2 - 4 sinx/2) dx equals

- 4√3 - 4
- 4√3 - 4 - π/3
- 2π/3 - 4 - 4√3
- π - 4

3
###
The integral is equal to: #02

The integral ∫(1 + x - 1/x)e^{x + 1/x} dx is equal to

- xe
^{x + 1/x}+ c - (x + 1)e
^{x + 1/x}+ c - (x - 1)e
^{x + 1/x}+ c - -xe
^{x + 1/x}+ c

4
###
If the integral ∫ (5 tan x / tan x − 2)dx = x + a ln |sin x - 2 cos x| + k

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
- 2
- -2
- 1

5
###
If g(x) = 0∫x cos4t dt, then g(x + π) equals

If g(x) = _{0}∫^{x} cos4t dt, then g(x + π) equals

- g(x) - g(π)
- g(x) / g(π)
- g(x) + g(π)
- g(x).g(π)

6
###
0∫π [cot x] dx, where [.] denotes the greatest integer function

_{0}∫^{π} [cot x] dx, where [.] denotes the greatest integer function, is equal to

- -π/2
- 1
- -1
- π/2

8
###
The area of the region bounded by the parabola (y – 2)^2 = x – 1, the tangent to the parabola

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

- 3
- 6
- 9
- 12

9
###
The integral is equal to: #01

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

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

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