#### Integral Calculus – II Important Questions

12th Standard EM

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Time : 01:00:00 Hrs
Total Marks : 50
10 x 1 = 10
1. Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

(a)

$\frac{30}{3}$ sq.units

(b)

$\frac{31}{3}$sq.units

(c)

$\frac{32}{3}$ sq.units

(d)

$\frac{15}{2}$ sq.units

2. The demand and supply functions are given by D(x)= 16 − x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is

(a)

2

(b)

3

(c)

4

(d)

5

3. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

(a)

9x2 + 54x

(b)

9x2 − 54x

(c)

54x - $\frac { { 9x }^{ 2 } }{ 2 }$

(d)

54x - $\frac { { 9x }^{ 2 } }{ 2 }$ + k

4. The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

(a)

40

(b)

$\frac{41}{2}$

(c)

$\frac{40}{3}$

(d)

$\frac{41}{5}$

5. The area unded by the curves y = 2x, x = 0 anx=2 is________sq.units.

(a)

loge2

(b)

3loge2

(c)

$\frac{3}{log_e2}$

(d)

2loge3

6. 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)

$\frac{5}{2}$

7. 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)

$\frac{\pi}{2}$

8. 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)

$\frac{3}{13}$

9. 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)

$\frac{16}{3}$

10. 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)

$\frac{2a^2}{3}$

11. 5 x 1 = 5
12. $\int _{ 0 }^{ t }{ 20,000t\quad dt }$

13. (1)

2x+5ex+k

14. $\int _{ 0 }^{ t }{ f(t)dt }$

15. (2)

55

16. $\int _{ 0 }^{ t }{(100-90x)dx }$

17. (3)

MR-MC

18. ഽ(2+5ex)dx

19. (4)

10,000t2

20. $\frac{dp}{dx}$

21. (5)

F(t)

5 x 2 = 10
22. Calculate the area bounded by the parabola y2 = 4ax and its latusrectum.

23. Find the area of the region lying in the first quadrant bounded by the region y = 4x2 , x = 0, y = 0 and y = 4

24. Find the demand function for which the elasticity of demand is 1

25. Find the consumer's surplus for the demand function p = 25 - x -x2 when Po = 19

26. Find the producer's surplus for the supply function p =r +x2 + 3 when xo =4

27. 5 x 3 = 15
28. The demand function of a commodity is y = 36 − x2. Find the consumer’s surplus for y0 = 11

29. Find the producer’s surplus defined by the supply curve g(x) = 4x + 8 when xo= 5.

30. Find the area of the region bounded by the line y = x - 5, the x-axis and between the ordinates x=3and x=7

31. The Marginal revenue for a commodity is MR=$\frac { { e }^{ x } }{ 100 } +x+{ x }^{ 2 }$, find the revenue function.

32. The marginal revenue function is given by $R'(x)=\frac { 3 }{ { x }^{ 2 } } -\frac { 2 }{ x }$. Find the revenue function and demand function if R(1)=6

33. 2 x 5 = 10
34. The price of a machine is 6,40,000 if the rate of cost saving is represented by the function f(t) = 20,000 t. Find out the number of years required to recoup the cost of the function.

35. Sketch the graph of y = Ix - 5|. Evaluate $\int _{ 0 }^{ 1 }{ |4x-5|dx }$