Using integration, find the area of the triangle ABC whose verti

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 Multiple Choice QuestionsShort Answer Type

41.

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

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 Multiple Choice QuestionsLong Answer Type

42.

Using integration, find the area of the triangular region whose sides have the equations y = 2 x + 1, y = 3 x + 1 and x = 4.

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43. Using the method of integration find the area of the region bounded by lines:
2 x + y = 4, 3 x - 2 y = 6 and x - 3 y + 5 = 0.
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44.

Using integration, find the area of the region bounded by (2, 5), (4, 7) and (6, 2).

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45. Using the method of integration, find the area of the triangle ABC, co-ordinates of whose vertices are A (2, 0), B (4, 5), C (6, 3).
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46.

Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 1), (0, 5) and (3, 2).

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47. Using integration, find the area of the triangle ABC whose vertices have coordinates A (3, 0), B(4, 6) and C (6, 2).


The given vertices are A (3, 0), B (4, 6), C (6, 2). The equation of AB is
                   straight y minus 0 space equals space fraction numerator 6 minus 0 over denominator 4 minus 3 end fraction left parenthesis straight x minus 3 right parenthesis
or                   straight y space equals 6 space left parenthesis straight x minus 3 right parenthesis
or                    straight y space equals space 6 straight x minus 18              ...(1)
The equation of BC is
                   straight y minus 6 space equals space fraction numerator 2 minus 6 over denominator 6 minus 4 end fraction left parenthesis straight x minus 4 right parenthesis
or                straight y minus 6 space equals space fraction numerator negative 4 over denominator 2 end fraction left parenthesis straight x minus 4 right parenthesis
or               straight y minus 6 space equals space minus 2 straight x plus 8
or                   straight y space equals space minus 2 straight x plus 14            ...(2)
The equation of CA is
                  straight y minus 2 space equals space fraction numerator 0 minus 2 over denominator 3 minus 6 end fraction left parenthesis straight x minus 6 right parenthesis space space or space space space straight y minus 2 space equals space fraction numerator negative 2 over denominator negative 3 end fraction left parenthesis straight x minus 6 right parenthesis
or              straight y minus 2 space equals 2 over 3 left parenthesis straight x minus 4 right parenthesis
or                   straight y space equals 2 over 3 straight x minus 2                 ...(3)
From B. C draw BM. CN ⊥ s on x-axis.
Required area = Area of ∆ AMB + Area of trap. MNCB - area of ∆ANC


                        equals space integral subscript 3 superscript 4 left parenthesis 6 straight x minus 18 right parenthesis space dx plus integral subscript 4 superscript 6 left parenthesis negative 2 straight x plus 14 right parenthesis space dx minus integral subscript 3 superscript 6 open parentheses 2 over 3 straight x minus 2 close parentheses space dx
equals space open square brackets 3 straight x squared minus 18 straight x close square brackets subscript 3 superscript 4 space plus space open square brackets negative straight x squared plus 14 straight x close square brackets subscript 4 superscript 6 space minus space open square brackets straight x squared over 3 minus 2 straight x close square brackets subscript 3 superscript 6
equals space left parenthesis 48 minus 72 right parenthesis minus left parenthesis 27 minus 54 right parenthesis plus left parenthesis negative 36 plus 84 right parenthesis minus left parenthesis negative 16 plus 56 right parenthesis minus left parenthesis 12 minus 12 right parenthesis plus left parenthesis 3 minus 6 right parenthesis
equals negative 24 plus 27 plus 48 minus 40 minus 0 minus 3 space equals space 8 space sq. space units. space

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48. Using integration, find the area of the triangle ABC whose vertices are A (3, 0) B (4, 5) and C (5, 1).
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 Multiple Choice QuestionsShort Answer Type

49.

Using integration, find the area of the region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).

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 Multiple Choice QuestionsLong Answer Type

50.

Using integration find the area of region bounded by the triangle whose vertices are (-1, 0), (1, 3) and (3, 2).

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