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Draw the sketch graph of the function y ...

Draw the sketch graph of the function `y =x^(2) ` and `y=x^(3) ` and shade the areas ` int _0 ^(1) x^(2) dx and int _0^(1) x^(3)dx ` what will be the value of the area enclosed by these two curves?

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The correct Answer is:
`(1)/(12)` square units
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CHHAYA PUBLICATION-DEFINITE INTEGRAL AS AN AREA-Long Answer type Questions
  1. (i) Using definite integral find the area of the triangle bounded by ...

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  2. Shade the area bounded by y^(2) =8x and y=x above positive direction ...

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  3. Draw the sketch graph of the function y =x^(2) and y=x^(3) and shade...

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  4. Show that,the area bounded by the parabola y^(2) =4ax and a double or...

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  5. Using integration ,find the area of the region enclosed between the ci...

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  6. Find the area of segment of the parabola y=x ^(2) -5x + 15 cut off by...

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  7. Mark the area bounded by the curve (y-1) (y-5) =4x and the y-axis and...

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  8. shade the area enclosed by the parabolas y^(2)=x and x^(2)=y and use ...

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  9. Using integration find the area of the regions common to the circle x...

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  10. Draw rough sketch of the area bounded by the curves x+2y=1 find its ar...

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  11. Find the common area between the parabolas y^(2) =4ax and x^(2) =4by

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  12. Determine the area enclosed between the parabola x^(2)=8y and the str...

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  13. Find the area of the region { (x,y):x^(2) +y^(2) lt 1lt x +y} (ii)...

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  14. Find the area included between the parabolas y^(2) =16x and the line ...

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  15. Show that,the area bounded between y=x^(3) and y=4x in the first quad...

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  16. Find the area in the first quadrant bounded by the circle x^(2) +y^(2)...

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  17. Find the area of the smaller part into which the circle x^(2) +y^(2) ...

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  18. The straight line bx+ ay =ab divides the ellipse b^(2) x^(2) +a^(2)...

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  19. If the area bounded by the parabola y^(2) =4ax and its double ordinat...

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  20. The area bounded in the first quadrant by the rectangular hyperbola xy...

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