Free Ncert Solutions for 12th Class Mathematics Application of integrals - Studyadda.com

s Free Ncert Solutions for 12th Class Mathematics Application of integrals - Studyadda.com

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12th Mathematics Application of integrals

1)

Find the area bounded by the curve y2 = x and the line x = 1, x = 4 and the x-axis.
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2)

Find the area bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
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3)

Find the area bounded by x2 =4ay, y = 2, y = 4 and the y-axis in the first quadrant.
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4)

Find the area bounded by the ellipse
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5)

Find the area bounded by the ellipse
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6)

Find the area in the first quadrant enclosed by x-axis, line and the circle x2 + y2 = 4.
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7)

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line
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8)

The area bounded between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
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9)

Find the area bounded by the parabola y = x2 and y = |x|.
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10)

Find the ara bounded by the curve x2 = 4y and the line x = 4y – 2.
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11)

Find the area bounded by the cure y2 = 4x and the line x = 3.
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12)

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.
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13)

Find the area bounded by curves (x – 1)2 + y2 =1and x2 + y2 = 1.
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14)

Find the area bounded by curves y = x2 + 2, y = x,x = 0 and x = 3.
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15)

Using integration, find the area bunded by the triangle whose vertices are (–1, 0), (1, 3), are (3, 2).
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16)

Using integration, find the area of triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.
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17)

Find the area under the given curves and given liens : (i) y = x2, x = 1, x = 2 and x - axis (ii) y = x4, x = 1, x = 5 and x –axis
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18)

Find the area between the curves y = x and y = x2.
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19)

Find the area in the first quadrant bounded by the curves y = 4x2, x = 0, y = 1 and y = 0.
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20)

Sketch the graph of y = |x + 3| and evaluate
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21)

Find the area bounded by the curve y = sin x between x = 0 and x =
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22)

Find the area enclosed between the parabola y2 = 4ax an the line y = mx.
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23)

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12.
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24)

Find the area of the smaller region bounded by the ellipse and the line
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25)

Find the area of the smaller region bounded by the ellipse and the line
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26)

Find the area enclosed by the parabola x2 = y and the line y = x + 2.
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27)

Using integrating, find the area bounded by the curve |x| + |y| = 1.
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28)

Find the area bounded by the curves {(x, y) ; } and y = |x|}
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29)

Using integration, find the area of the triangle whose vertices are A(2, 0), B(4, 5), C(6, 3).
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30)

Using integration, find the area bounded by the lines : 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0
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31)

Find the area of the region {(x, y) :
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