application of integration

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APPLICATION OF INTEGRALS - NCERT SOLUTIONS

Question 1:
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the xaxis.
ANSWER

The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD.

Question 2:
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant. ANSWER

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The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-axis is the area ABCD.

Question 3:
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant. ANSWER

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The area of the region bounded by the curve, x2 = 4y, y = 2, and y = 4, and the y-axis is the area ABCD.
Question 4:
Find the area of the region bounded by the ellipse
ANSWER
The given equation of the ellipse,

, can be represented as

Question 5:
Find the area of the region bounded by the ellipse
ANSWER
The given equation of the ellipse can be represented as

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It can be observed that the ellipse is symmetrical about x-axis and y-axis.
∴ Area bounded by ellipse = 4 × Area OAB

Therefore, area bounded by the ellipse =
Question 6:
Find the area of the region in the first quadrant enclosed by x-axis, line

and the

circle
ANSWER
The area of the region bounded by the circle,
OAB.

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, and the x-axis is the area

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The point of intersection of the line and the circle in the first quadrant is
Area OAB = Area ΔOCA + Area ACB

.

Area of OAC
Area of ABC

Therefore, area enclosed by x-axis, the line

, and the circle

in the first

quadrant =
Question 7:
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line
ANSWER

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