Find the area bounded by the curve y = cos x between x = 0 and

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 Multiple Choice QuestionsLong Answer Type

31. Find the area of the region enclosed by the parabola y2 = 4 a x and the line y = mx.
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32.

Find the area bounded by the curve  y = x2 and the line y = x.
OR
Find the area of the region {(x. y): x2 ≤ y ≤ x}.

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33. Using the method of integration find the area bounded by the curve |x| + |y| = 1.
[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].


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34.

Find the area of the region bounded by the line y = 3 x + 2, the x-axis and the ordinates x = - 1 and x = 1.

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35. Find the area of the region included between the parabola straight y space equals 3 over 4 straight x squared space and space the space line space 3 straight x space minus space 2 straight y space plus space 12 space equals space 0
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36. Find the area bounded by the parabola x2 = 4 y and the straight line x = 4 y - 2.
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37. Find the area of the region included between the parabola y2 = x and the line x + y = 2.
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38.

Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and the x-axis.
OR
Draw the rough sketch and find the area of the region:
{(x, y): x2 < y < x + 2}

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 Multiple Choice QuestionsShort Answer Type

39.

Draw a rough sketch of the curves y = sin x and y = cos x as x varies from 0 to straight pi over 2 and find the area of the region enclosed by them and the x-axis.

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40.

Find the area bounded by the curve y = cos x between x = 0 and x = 2 straight pi.


The equation of curve is
y = cos x
Its rough sketch from x = 0 to x = 2 straight pi is shown in figure.

Required area = area of the region OABO + area of the region BCDB + area of the region DEFD.
equals space integral subscript 0 superscript straight pi over 2 end superscript cos space 2 straight x space dx space plus space open vertical bar integral subscript straight pi over 2 end subscript superscript fraction numerator 3 straight pi over denominator 2 end fraction end superscript cosx space dx close vertical bar space plus space integral subscript fraction numerator 3 straight pi over denominator 2 end fraction end subscript superscript 2 space straight pi end superscript space cos space straight x space dx
equals space open square brackets sin space straight x space close square brackets subscript 0 superscript straight pi over 2 end superscript space plus space open vertical bar open square brackets sin space straight x close square brackets subscript straight pi over 2 end subscript superscript fraction numerator 3 straight pi over denominator 2 end fraction end superscript close vertical bar space plus space open square brackets sin space straight x close square brackets subscript fraction numerator 3 straight pi over denominator 2 end fraction end subscript superscript 2 space straight pi end superscript
space equals space open parentheses sin space straight pi over 2 minus sin space 0 close parentheses space plus space open vertical bar open parentheses sin space fraction numerator 3 straight pi over denominator 2 end fraction minus sin space straight pi over 2 close parentheses close vertical bar space plus space open parentheses sin space 2 straight pi space minus space sin space fraction numerator 3 straight pi over denominator 2 end fraction close parentheses
equals space left parenthesis 1 minus 0 right parenthesis space plus space open vertical bar negative 1 minus 1 close vertical bar space plus space left parenthesis 0 plus 1 right parenthesis
equals space 1 plus open vertical bar negative 2 close vertical bar space plus space 1 space equals space 1 plus 2 plus 1 space equals space 4

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