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Find the area of the portion enclosed be...

Find the area of the portion enclosed between the curves `y^2=4x` and `x^2=4y`.

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To find the area of the portion enclosed between the curves \( y^2 = 4x \) and \( x^2 = 4y \), we will follow these steps: ### Step 1: Identify the curves The first curve is \( y^2 = 4x \), which is a rightward-opening parabola. The second curve is \( x^2 = 4y \), which is an upward-opening parabola. ### Step 2: Find the points of intersection To find the points where these two curves intersect, we can solve the equations simultaneously. ...
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MAHAVEER PUBLICATION-APPLICATION OF INTEGRALS-QUESTION BANK
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  2. Find by the method of integration the area of the region bounded by th...

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  3. Find the area of the portion enclosed between the curves y^2=4x and x^...

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  4. Find the area of the regions bounded by the parabola y^2=4ax and the l...

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  5. Find area under the curve y=sin 2x between the ordinates x=pi/2 and x=...

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  6. Find by integration, the area of the triangle bounded by the lines 4y-...

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  7. Find the center and radius of the circle x^2+y^2+8x+10y-8=0.

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  8. Find the equation of the parabola with vertex (0,0) and passing throug...

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  9. In what ratio does the origin divides the line segment joining the poi...

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  10. Find the direction cosines of the line whose direction ratios are 2,-4...

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  11. If g(x)=2^x, show that g(a).g(b) = g(a+b).

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  12. Find lim(x rarr2)(x^2-9x+14)/(x^2+9x-22)

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  13. Examine the continuity of f(x) at x=0 if f(x)=(sin 2x)/(2x), x ne 0

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  14. Find dy/dx:y= sqrt (1+x^2)

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  15. Find dy/dx: x=(2at)/(1+t^2), y=(a(1-t^2))/(1+t^2)

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  16. Find dy/dx if xy=sinx.

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  17. Find the maximum and minimum values of the function y=4x^3 -15x^2 +12x...

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  18. Find the unit vector in the direction of the vector vec a + vec b if v...

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  19. Integrate: int cos ecx (cos ecx +cot x) dx

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  20. Integrate: int 6x(3x^2+7)^7 dx

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