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The area enclosed between the lines x = 2 and x = 7 is
Area enclosed between the lines x = 2 and x = 7 is Infinite.
If the area of y = f(x) between x = a and x = b is then the point c is the point of intersection of the curve with:
Area under the circle x2 + y2 = 16 is
Area of the shaded region in the given figure is :
Area of the region bounded by the curve y2 = 2y –x and y-axis is:
y2 = 2y −x ⇒x = 2y −y2 Curve meets y −axis where x= 0 2y −y2 = 0 ⇒y (2 −y) = 0 y = 0 or y = 2 Area =∣∫(0 to 2) x.dy ∣ =|∫(0 to 2) (2y −y2 ).dy ∣ =∣[y2 −y3 /3] (0 to 2) |[4 −8/3]−0| =4/3 unit2
The area of the region bounded between the line x=9 and the parabola y2 =16x is
Correct Answer : a
Explanation : Equation of the parabola is
y2 = 16x .... (i)
Required area =2 ∫(0 to 9) ydx
[by symmetry about x-axis]
= 2 ∫(0 to 9) 4(x)1/2 dx
= 8 ∫(0 to 9) (x)1/2 dx
= 8[(x3/2 )/(3/2)](0 to 9)
= 16/3[x3/2 ](0 to 9)
= 144 sq unit.
Area of the region is :
If the area above x-axis, bounded by the curves y = 2kx , x = 0 and x = 2 is then k = ?
Write the shaded region as an integral
The area bounded by the curve:
y = cos2 x between x = 0, x = π and x axis
y = cos2 x [0,π] ∫(0 to π/2)cos2 xdx + ∫(π/2 to π)cos2 xdx = 1/2 ∫(1 + cos 2x) = [½(x + sin(2x)/2](0 to π/2] + [1/2(x + sin(2x)/2](π/2 to π) = ½|π+ 0 - 0 - 0| + 1/2|(π+ 0) - π/2|= π/4 + π/4 = π/2
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