Download = 3, y 1 x 1 x, + + − x = = 4y 3x by the line 2y 3x+12

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APLICATION OF INTGRALS--- WORD PROBLEMS
1.
Using integration find area of the region bounded by y = 1 + x + 1 , x = −3, x
= 3, y = 0
2.
Using integration, find the area cut off from the
parabola 4y = 3x 2 by the line 2y = 3x+12.
3.
Find the area of the region bounded the curves x = 2y − y 2 and y = 2+x
using integration.
4.
Draw a rough sketch and find the area bounded by y = x 2 − x and y=4x − x 2
using integration.
5.
Sketch the region bounded by the curves y = 5 − x 2 and = x − 1 and find its
area using integration.
6.
Make a rough sketch of the region and find its area using
}
{
integration: ( x , y ) 0 ≤ y ≤ x 2 + 3, 0 ≤ y ≤ 2x+3,0 ≤ x ≤ 3
7.
Find area of the region bounded by y = x 2 + 2 and y 3 = x − 2, x = 0 using
integration.
8.
Using integration find the area of the
{
region: ( x, y ) : y 2 ≤ 6ax and x 2 + y 2 ≤ 16a 2
9.
}
Using integration find the area of the region bounded bound by the triangle ABC,
using equation of whose sides are y = 2x + 1, y = 3x+1 and x = 4.
10.
Find the region bounded by two parabolas y 2 = 5x and x 2 = 5y using
integration.
11.
Find area of the smaller region bounded by the curves
x 2 + y 2 = 4 and y 2 = 3 ( 2x − 1) using integration.
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ASSIGNMENTS AT TUTORBREEZE.COM
Mathematics Class 12
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Classes 5-12 at TutorBreeze.com.
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____________________________________________________________________________________________________________
12.
Find the area bounded by the curves y = tan x , x ∈
x∈
13.
−π π
, and y = cotx,
3 3
5 5y
,
and the axis.
6 6
Find the area bounded by the curves Y 2 = 4a 2 ( x − 1) and the lines x = 1 and
y = 4a
14.
Draw a rough sketch of the curves y = cos x when x ∈ 0,
π
and find area of the
2
region enclosed by them and x-axis.
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ASSIGNMENTS AT TUTORBREEZE.COM
Mathematics Class 12
Write to me at [email protected] for more information on live online tutoring in Mathematics, Physics, Chemistry for students of
Classes 5-12 at TutorBreeze.com.
Study from the Best Teachers to get the Best Result!
____________________________________________________________________________________________________________
ANSWERS: DEFINITE INTEGRALS – word problems
9
sq. units
2
6.
26
sq . units
3
16 sq. units
2.
4.
125
24
5.
7.
17
sq. units
4
8.
4a 2
4π + 3 sq. units
3
9.
8 sq. units
10.
25
sq. units
3
11.
4π
1
−
sq. units
3
3
12.
log 2 sq. units
13.
16a
sq. units
3
14.
(2 − 2 ) sq. units
sq. units
27 sq. units
3.
1.
5π 1
−
4 2
sq. units
(
)
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