Areas of Bounded Regions Exercise - I | Answer Key

University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2022
Views:

148

Pages:

1
Author:

Origbo2ol

AREAS OF BOUNDED REGIONS EXERCISE – I UNSOLVED PROBLEMS Q.1 Using integration, find the area of the region bounded by the lines y = 4x + 5, y = 5 – x and 4y – x = 5. Q.2 Find the area of the region bounded by the curve x2 = 4y and the lines x = 4y – 2 Q.3 Find the area of the region bounded by the curve y = x2 + 2, y = x, x = 0 and x = 3 Q.4 Find the area of the region enclosed between the parabola y2 = x and the line x + y = 2 in the first quadrant. a Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line x = 2 Q.5 Q.6 Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32. Q.7 Find the area of the region bounded by the curve y  1  x 2 , the line y = x and the positive x-axis. Q.8 Find the area of the smaller region bounded by the ellipse Q.9 Find the area included between the curves y2 = 4ax and x2 = 4ay, a > 0 Q.10 Draw the rough sketch of y2 = x + 1 and y2 = – x + 1 and determine the area enclosed by the two curves. Q.11 Calculate the area of the region enclosed between the circle x2 + y2 = 4 and (x – 2)2 + y2 = 4 Q.12 Using integration, find the area of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x Q.13 Sketch the region common to the circle x2 + y2 = 16 and the parabola x2 = 6y. Also find the area of the region, using integration Q.14 Sketch the graph of y = |x + 3|. Evaluate x y x2 y2   1 and the line   1 a b a2 b2 0 the graphs ?  | x  3 | dx What does the value of the integral represent on –6 Q.15 Using integration find the area of the region bounded by the following curves after making a rough sketch : y = 1 + |x – 1|, x = – 3, x = 3 and y = 0 Q.16 Find the area of the region {(x, y) : x2 + y2  1  x + y} Q.17 Find the area of the region {(x, y) : x2  y  |x|} Q.18 Find the area of the region : {(x, y) : 0  y  (x2 + 1), 0  y  (x + 1)}, 0  x  2} Q.19 Find the area of the region : {(x,y) : x2 + y2  2ax}, y2  ax, x  0, y  0 Q.20 Find the area bounded by the curve y = sin x between x = o and x = 2. 1. 9. 15 2 16a2 3 15. 16 Answers 2. 10. 9 8 3. 21 4. 2 8 3   1 16.    4 2 7 a 2    1 5. 6 2 2   8  2 3 11.   3  1 17. 3 23 18. 6 6. 4 7. 12.  8 4  3 8  3 8. 13. ab ab – 4 2 16   4 3 3  a2 2a 2    19.  4  3    14. 9 20. 4