The area bounded by y = 2x - x² and X-axis is _________ sq. units

(a)

\(\frac{2}{3}\)

(b)

\(\frac{4}{3}\)

(c)

2

(d)

4

The area of the region bounded by the ellipse __________

(a)

\(\pi\)ab sq.units

(b)

\(\frac{\pi a}{b}\) sq.units

(c)

2\(\pi\)ab sq.unit

(d)

\(\frac{\pi}{2}\) ab sq.units

The area unded by the curves y = 2^x, x = 0 and x = 2 is________sq.units.

(a)

log_e2

(b)

3log_e2

(c)

\(\frac{3}{log_e2}\)

(d)

2log_e3

The area of the region bounded by the line 2y = -x + 8, X - axis and the lines x = 2 and x = 4 is ________ sq.units.

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{5}\)

(c)

5

(d)

\(\frac{5}{2}\)

The area enclosed by the curve y = cos²x in [0,\(\pi\)] the lines x=0, x = \(\pi\) and the X-axis is ________sq.units.

(a)

2\(\pi\)

(b)

2\(\pi\)

(c)

\(\frac{2}{\pi}\)

(d)

\(\frac{\pi}{2}\)

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

(a)

\(\frac{13}{3}\)

(b)

13

(c)

\(\frac{26}{3}\)

(d)

\(\frac{3}{13}\)

The value of \(\int _{ -3 }^{ 2 }{ |x+1| } dx\) is______.

(a)

4

(b)

\(\frac{1}{4}\)

(c)

8

(d)

2

The area lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units

(a)

\(\frac{16}{3}\)

(b)

\(\frac{8}{3}\)

(c)

\(\frac{32}{3}\)

(d)

\(\frac{64}{3}\)

The area of the region bounded by the curve y² = 2y - x and the y-axis _____ sq. units

(a)

\(\frac{4}{3}\)

(b)

\(\frac{2}{3}\)

(c)

4

(d)

\(\frac{16}{3}\)

The area bounded by the curve y = 4ax and the lines y² = 2a and Y-axis is _______ sq. units.

(a)

\(\frac{2a}{3}\)

(b)

2a²

(c)

\(\frac{a^2}{3}\)

(d)

\(\frac{2a^2}{3}\)

If the marginal cost function MC = 2 - 4x, then the cost function is _________

(a)

2x- 2X²+ k

(b)

2-4x²

(c)

\(\frac{2}{x}-4\)

(d)

2x-4x²

If MR = 15 - 8x, then the revenue function is _________

(a)

15x - 4x² + k

(b)

\(\frac{15}{x}-8\)

(c)

-8

(d)

15x - 8

If R' (x) = \(\frac{1}{x+1}\), then the revenue function is_________

(a)

log|x+1|+k

(b)

\(\frac{-1}{x+1}\)

(c)

\(\frac{1}{(x+1)^2}\)

(d)

log\(\frac{1}{x+1}\)

The Consumer's surplus for the demand function P =f(x) for the quantity X_o and price P_o is_________

(a)

\(\int _{ 0 }^{ x0 }{ f(x)dx-{ p }_{ 0 }{ x }_{ 0 } } \)

(b)

\(\int _{ 0 }^{ x0 }{ f(x)dx } \)

(c)

p₀x₀-\(\int _{ 0 }^{ x0 }{ g(x)dx } \)

(d)

\(\int _{ 0 }^{ p0 }{ f(x)dx } \)

The Producer's surplus for the supply function P = g(x) for the quantity X_o and price P_o is_________

(a)

\(\int _{ 0 }^{ x0 }{ g(x)dx } -{ p }_{ 0 }{ x }_{ 0 }\)

(b)

\({ p }_{ 0 }{ x }_{ 0 }-\int _{ 0 }^{ x0 }{ g(x)dx } \)

(c)

\(\int _{ 0 }^{ x0 }{ g(x)dx } \)

(d)

\(\int _{ 0 }^{ p0 }{ g(x)dx } \)