Find the area of the region bounded by y2 = 4 x, x = 1, x = 4

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 Multiple Choice QuestionsShort Answer Type

1. Find the area of the region bounded by the curve y= x and the lines x = 1, x = 4 and the x-axis in the first quadrant.
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2.

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


The equation of curve is y2 = 4 x
Required area  = integral subscript 1 superscript 4 straight y space dx
            equals space integral subscript 1 superscript 4 2 square root of straight x space dx space equals space 2 integral subscript 1 superscript 4 straight x to the power of 1 half end exponent dx
equals space 2 open square brackets fraction numerator straight x 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 1 superscript 4 space equals space 4 over 3 open square brackets straight x to the power of 3 over 2 end exponent close square brackets subscript 1 superscript 4 space equals space 4 over 3 open square brackets open parentheses 4 close parentheses to the power of 3 over 2 end exponent minus 1 close square brackets
equals space 4 over 3 left parenthesis 8 minus 1 right parenthesis space equals space 4 over 3 cross times 7 space equals space 28 over 3 space sq. space units


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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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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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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
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6.

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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9.

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.
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