7/28/2019 Definite Integral and AREAunder Curve

1/2

7/28/2019 Definite Integral and AREAunder Curve

2/2

16. Show that ( ) =+2

02cottan

dxxx

17. Draw a rough sketch of the region ( ) 1633,3;, 222 + yxxyyx and find the area

enclosed by the region using method of integration.

6

2739

4

3sin

3

16

3

16

3

8

3

4.

1223 +=

+ awhere

aaaaAns

18. Find the area of the smaller region bounded by the ellipse 12

2

2

2

=+b

y

a

xand the line

1=+b

y

a

x

unitssqab

abAns .

2

1

4.

19. Draw a rough sketch and find the area of the region bounded by two parabolas

yxandxy 4422 == by using method of integration.

..3

16. unitssqAns

20. Using integration, find the area of the region enclosed between the circles

( ) 424 2222 =+=+ yxandyx

unitssqAns .323

8.

21. Using integration, find the area bounded by the lines 721,22 =+==+ yxandxyyx

[ ]..6. UnitssqAns

22. Using integration, find the area of the triangular region whose vertices are (1, 0),

(2, 2) and (2, 1).

..2

3. unitssqAns

23. Find the area bounded by the curve yx 42 = and the straight line .24 = yx

..8

9. unitssqAns

***