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Application of Integrals

Short Answer Type

1. Find the area of the region bounded by the curve y²= x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

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Find the area of the region bounded by y² = 4 x, x = 1, x = 4 and the x-axis in the first quadrant.

821 Views

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

752 Views

4.
Find the area of the region bounded by y² = x - 2, x = 4, x = 6 and the x-axis in the first quadrant.

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The equation of curve is y² = x - 2. which is right handed parabola with vertex at (2, 0).
Two lines are x = 4 and x = 6
Required area = Area ABCD
$equals space integral subscript 4 superscript 6 straight y space dx space equals space integral subscript 4 superscript 6 square root of straight x minus 2 end root dx equals space integral subscript 4 superscript 6 left parenthesis straight x minus 2 right parenthesis to the power of 1 half end exponent dx equals space open square brackets fraction numerator left parenthesis straight x minus 2 right parenthesis to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 4 superscript 6 space equals space 2 over 3 open square brackets left parenthesis straight x minus 2 right parenthesis to the power of 3 over 2 end exponent close square brackets subscript 4 superscript 6 equals space 2 over 3 open square brackets 4 to the power of 3 over 2 end exponent minus 2 to the power of 3 over 2 end exponent close square brackets space equals space space 2 over 3 left parenthesis 8 minus 2 square root of 2 right parenthesis space sq. space units$

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5. Find the area under the given curves and given lines:
(i) y = x², x = 1, x = 2 and x-axis
(ii) y - x^4, x = 1, x = 5 and x -axis

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

275 Views

7. Find the area of the region lying in the first quadrant and bounded by y = 4 x², x = 0, y = 1 and y = 4.

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8. Find the area of the region lying in the first quadrant and bounded by x² = y - 3, y = 4, y = 6 and the y-axis in the first quadrant.

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Find the area of the region bounded by x² = 16 y, y = 1, y = 4 and the y-axis in the first quadrant.

317 Views

10. Find the area bounded by the curve y² = 4 a (x-1) and the lines x = 1 and y = 4 a.

315 Views

Previous Year Papers

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Test Yourself

Short Answer Type

4. Find the area of the region bounded by y2 = x - 2, x = 4, x = 6 and the x-axis in the first quadrant.

4.
Find the area of the region bounded by y² = x - 2, x = 4, x = 6 and the x-axis in the first quadrant.