Eamcet - Maths - Definite Integration

The area bounded by x=0,x=6+5y-y2 is

A.  517/6

B.  278/3

C.  280/3

D.  343/6

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The area between the curves y2=8x and x2=8y is

A.  64/3

B.  34/3

C.  64/5

D.  35/3

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The area bounded by y=cos x,y=x+1,y=0 is

A.  3/2

B.  2/3

C.  1/2

D.  5/2

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The variable line x/a+y/b=1 is such that a+b=10, the locus of the midpoint of the portion of the line intercepted between the axes is:

A.  x+y=10

B.  10x+5y=1

C.  x+y=5

D.  5x+10y=1

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The area between the parabola y=x2 and the line y=2x is

A.  1/3

B.  8/3

C.  1/2

D.  4/3

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The value of c for which the area bounded by the curve y=8x2-x5,the lines x=1,x=c and x-axis is 16/3 is

A.  1

B.  0

C.  -1

D.  -2

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The area of the region bounded by the curves y=x2+2,y=x,x=0 and x=3 is

A.  4/3 sq.unit

B.  2/3 sq.unit

C.  21/2 sq.unit

D.  27 sq.unit

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The area of the plane region bounded by the curve x + 2y2 = 0 and 3y2 = 1 is equal to

A.  2/3

B.  4/3

C.  5/3

D.  1/3

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The area bounded by the curve y2=4x and the lines x=1,x=9 is

A.  436/15

B.  208/3

C.  236/5

D.  340/13

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If a is the area bounded by the curve y=4x-x2-3 with x-axis,b is the area bounded by y=11x-24-x2 with x-axis and c is the area bounded by y=(x-4)(x-1) with x-axis then the descending order of a,b,c is

A.  a,b,c

B.  b,c,a

C.  a,c,b

D.  c,a,b

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If y = sin (logex) then x2 (d2y/dx2) + x (dy/dx) =

A.  sin (logex)

B.  cos (logex)

C.  y2

D.  - y

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The area of the region bounded by the curve y=x3,x-axis and the ordinates x=1,x=4 is

A.  255/4

B.  155/4

C.  55/4

D.  355/4

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The area bounded by the curve x=y2 +4y with y-axis is

A.  28/3

B.  32/3

C.  13/6

D.  23/3

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If area bounded by the curves y2=4ax and y=mx is a2/3,then the value of m is

A.  2

B.  -2

C.  1/2

D.  none

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The area of the region bounded by the curve y=(x2+2)2+2x between the ordinates x=0,x=2 is

A.  436/15

B.  208/3

C.  236/5

D.  340/13

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If a is the area bounded by x=4-y2 with y-axis,b is the area bounded by x=6+5y-y2 with y axis and c is the area bounded by 2x=y2-1 with y-axis then the ascending order of a,b,c is

A.  a,b,c

B.  b,c,a

C.  a,c,b

D.  c,a,b

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The area bounded by the curve xy=4,x-axis and the ordinates x=2,x=5 is

A.  2 log 5/2

B.  4 log 5/2

C.  5 log 5/2

D.  3 log 5/2

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The area under the curve y=x2-3x+2 with boundaries as x-axis and the ordinates at x=0,x=3 is

A.  3/8

B.  2/3

C.  3/5

D.  9/2

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The area bounded by the curves y=3x-x2 and y=x2-x is

A.  1/3

B.  8/3

C.  1/2

D.  4/3

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The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is

A.  10/3

B.  5/3

C.  20/3

D.  none

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The area of the region bounded by the curve y2=4x,y-axis and the lines y=1,y=3 is

A.  28/3

B.  32/3

C.  13/6

D.  23/3

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