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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.

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

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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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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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(i) The given curve and lines are
y = x², x = 1, x = 2 and x-axis
Required area = $integral subscript 1 superscript 2 straight y space dx space equals space integral subscript 1 superscript 2 straight x squared dx space equals space open square brackets straight x cubed over 3 close square brackets subscript 1 superscript 2 space equals space 8 over 3 minus 1 third space equals space 7 over 3$
(ii) The given curve and lines are
y = x⁴, x = 1, x = 5 and x-axis
Required area = $integral subscript 1 superscript 5 straight y space dx space space equals space integral subscript 1 superscript 5 straight x to the power of 4 dx space space equals open square brackets straight x to the power of 5 over 5 close square brackets subscript 1 superscript 5 space equals space fraction numerator left parenthesis 5 right parenthesis to the power of 5 over denominator 5 end fraction minus fraction numerator left parenthesis 1 right parenthesis to the power of 5 over denominator 5 end fraction space space space space space space space space space space space space space space space space space equals 3125 over 5 minus 1 fifth space equals space 3124 over 5 space sq. space units.$

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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.

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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.

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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

Test Series

Test Yourself

Short Answer Type

5. Find the area under the given curves and given lines:(i) y = x2, x = 1, x = 2 and x-axis(ii) y - x4, x = 1, x = 5 and x -axis

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