Areas of Bounded Regions Exercise - II

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

2022
Views:

224

Pages:

1
Author:

lorenzops0

AREAS OF BOUNDED REGIONS EXERCISE – II Q.1 Q.2 Q.3 Q.4 Q.5 BOARD PROBLEMS Using integration, find the area of the region, given : {(x, y) : 0  y  x2 + 1 ; 0  y  x + 1, 0  x  2} Using integration, find the area of PQR where P is (2, 1) Q is (3, 4) and R is (5, 2) Using integration, find the area of the region bounded by the line 2y + x = 8, x-axis and the line x = 2 sand x = 4. Find the area of the region given by {(x, y) : x2  y  |x|}. Using integration, find the area of triangle ABC, whose vertices are A(3,0), B(4, 5) and C(5, 1) Q.6 Find the area of the following region : {(x, y) : y2  4x, 4x2 + 4y2  9}. Q.7 Q.8 Using integration, find the area of the region in the first quadrant enclosed by the x-axis and the line y = x and the circle x2 + y2 = 32. Find the area of the region lying between the parabola y2 = 4ax and x2 = 4ay, where a > 0 Q.9 Using integration, find the area of the smaller region bounded by the Q.10 x y x2 y2  1   1 and the straight line 4 3 16 9 Find the area enclosed by the parabola y2 = x and the line x + y = 2 and the x-axis. Q.11 Using integration, find the area of the smaller region bounded by the ellipse curve x2 y2  1 a2 b2 x y  1 a b Using integration, find the area of the region enclosed between two circles x2 + y2 = 1 and (x – 1)2 + y2 =1. Using integration, find the area of the region enclosed between the circles x2 + y2 = 1 and (x – 1)2 + y2 = 1. Find the area of that part of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x. Find the area of the region bounded by the parabolas y2 = 4ax and x2 = 4ay. Using integration, find the area of the region enclosed between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4. Find the area of the region included between the parabola y2 = x and the line x + y = 2. Using the method of integration, find the area of the region bounded by the lines 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0 Find the are of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y. Using integration, find the area of the triangle ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4). Sketch the graph of y = |x + 3| and evaluate the area under the curve y = |x + 3| above x-axis and between x = – 6 to x = 0. Find the area of the region : {(x, y) : x2 y2 4, x + y  2}. Find the area of the region bourded by the parabola y = x2 and y = |x| and the straight line Q.12 Q.13 Q.14 Q.15 Q.16 Q.17 Q.18 Q.19 Q.20 Q.21 Q.22 Q.22 1. 23 6 Answers 2. 4 3. 5 7. 4 8. 16/3 9. 3( – 2)  2 3   13.  3  2    14. 4 (8 – 3 4. 16 2 3 ) 15. 3 a 1 3 5. 9/2 10. 7/6 11. 6. 1 3 2 ab (   2) 4  8  2 3 16.  3   21. 9 + 12. 9 9 –1 1 – sin 8 4 3 2 3 – 3 2 22. ( – 2)