Integration(Senior Class Math Study by Topics Test ) : GATE Academy

Welcome to your Integration(Senior Class Math Study by Topics)

NAME

PHONE NUMBER

1. Find
∫x tan²x dx

Incos x+C

x(tanx- x) +In cosx + x²/2 + C

x(tanx- x) +In cosx + C

x(tanx -x) + C

2. Evaluate the definite integral:

102

3. An object travels in a straight line with velocity, v m/s at time t s is given by v = 3t² + 7. What is the distance travelled by the object from t = 2 s to t = 5 s?

144 m

112 m

138 m

168 m

4. Using the trapezoid rule with five ordinates
at x = 1, 2, 3, 4, 5, estimate the value of

10 sq. units

13 sq. units

11 sq. units

12 sq. units

5. The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the equation of the curve

2x² + 3x + 1

y³/3 - 2x² + 3x + 1

y³/3 - 2x² + 3x + 6

y³/3 - 2x²

6. Evaluate:

283/3 sq units

38/3 sq. units

283 sq. units

48 sq. units

7. Evaluate:

0.777

0.658

0.163

0.563

8. Evaluate:

12/5

1/2

12/7

14/3

9. Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.

4/3

10. A curve passes through the point (3, -1).
If its gradient function is 2x + 5,
find the equation of the curve

y = x² + 5x - 25

y = 3x³ + x² + 5x - 25

y = 3x³ + 5x - 25

y = 3x³ + x² + 5x + 25

11. Evaluate the integrals:

-1/5

-1/2

1/2

1/5

12. Evaluate:

correct to 3 decimal places

2.868

3.797

2.368

2.386

13. The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the minimum point on the curve

(2, 9)

(3, 1)

(0, 6)

(1, 7)

14. A particle moves in a straight line with a velocity v in m/s at time t is given by v = 3t² +10. Calculate the distance it travels from t = 2s to t = 5s.

32 m

147 m

47 m

132 m

15. The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero.

1/2s, 2.4s

-2s, 9s

0s, 4s

3s, 5s

16. Given that y and x are two variables such that dy/dx = 2x - 6, and y = -1 when x = 3, express y in terms of x.

y = x² - 6x + 8

y = x² + 6

y = x² + 6x + 8

y = x - 3

17. Find
∫x sinx dx

-x cosx + sinx + C

cos x + sinx + C

sinx + C

1/x + C

18. A curve y has gradient
dy/dx = 3x² - 6x + 2.
If the curve passes through the origin,
find its equation.

y = x(x-1)(x-2)

y = 1-x

y = x(x+5)

y = x + 2

19. Evaluate the definite integral:

-4

20. Find the area of the region lying below the x-axis and bounded by the parabola
y = x(x - 2) and the x-axis.

4/3

3/4

3/2

2/3

21. Evaluate the integrals:

22. A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Determine the coordinates of M and N

M(2, 5), N(3, 18)

M(2, 3), N(2, 5)

M(1, 3), N(3, 12)

M(0, 4), N(4, 18)

23. The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the maximum point on the curve

(4, 0)

(1, 2)

(11/3, 9)

(1, 7/3)

24. Find the area bounded by the given pairs of curves y = x² - x + 3 and y = 3

1/5

1/3

1/6

1/2

25. Calculate the area of the finite region bounded by the curve
y = x² + 4x - 12, the x-axis and the ordinates x = 1 and x = 3

26 out of 25