# Integration

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

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

### The integral is equal to: #03

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

### The integral is equal to: #02

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

### 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. -1
2. 2
3. -2
4. 1

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

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)

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

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

1. -π/2
2. 1
3. -1
4. π/2

### ∫ |sin x| dx is

010π |sin x| dx is

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

### 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

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

### The integral is equal to: #01

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