Area Bounded by Curves

IMPORTANT

Area Bounded by Curves: Overview

This topic covers concepts, such as, Area under Simple Curves, Area Included between the Curve y=f(x), Prismoidal Formula & Simpson's Rule etc.

Important Questions on Area Bounded by Curves

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The area of the region between the curves   y= 1+sinx cosx  and   y= 1sinx cosx  bounded by the lines   x=0  and   x= π 4  is:

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The area bounded by the parabolas   y= (x+1) 2  and   y= (x1) 2  and the line y = 1/4 is:

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The area enclosed between the curves y=ax2  and x=ay2(a>0) is 1 square unit, then the value of a is:

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The area bounded by the curves   y= x ,2y+3=x  and x-axis in the   1 st quadrant is:

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If area bounded by the curves  y=fx (which lies above x-axis x1), the x-axis and the ordinates  x=1 & x=b is b-1sin3b+4 sq. units b>1, then fx is

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Let the area bounded by the x-axis, curve y=1+8x2 and the ordinates x=2 and x=4 is "A" sq. unit and if the ordinate x=a divides the area into two equal parts, then the correct statement among the following is

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For any real   t,x= e t + e t 2 ,y= e t e t 2  is a point on the hyperbola   x 2 y 2 =1.  Find the area bounded by this hyperbola and the lines joining its centre to the points corresponding to   t 1 and t 1  is  

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Find the area bounded by the curves   x 2 + y 2 =4.

  x 2 = 2 yandx=y,

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The area of the region bounded by the curves y=5x2 and y=x1 is (in sq. units)

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If A is the area in the first quadrant enclosed by the curve C:2x2-y+1=0, the tangent to C at the point 1, 3 and the line x+y=1, then the value of 60A is................

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Let the area enclosed by the lines x+y=2, y=0, x=0 and the curve f(x)=minx2+34,1+[x] where [x] denotes the greatest integer x, be A. Then the value of 12A is

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The area of the region x,y:x2yx2-4,y1 is

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If the area bounded by the curve 2y2=3x, lines x+y=3, y=0 and outside the circle x-32+y2=2 is A, then 4π+ 4A is equal to __________.

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The area of the region enclosed by the curve fx=max{sinx,cosx},-πxπ and the x-axis is

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If the area of the region x,y:x2-2yx is A, then 6A+162 is equal to ______________

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Area of the region x,y:x2+y-224,x22y is

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The area of the region enclosed by the curve y=x3 and its tangent at the point (1, 1) is

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Let y=px be the parabola passing through the points 1, 0, 0, 1 and 1, 0. If the area of the region x, y:x+12+y-121, ypx is A, then 12π-4A is equal to ________ .

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If the area of the region S=(x,y):2y-y2x22y,xy is equal to n+2n+1-πn-1, then the natural number n is equal to _______

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The area of the region x,y: x2y8-x2,y7 is