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Find the area between the x-axis and the...

Find the area between the x-axis and the curve `y=sinx` from `x=0` to `x=2pi`

A

4 square units

B

2 square units

C

`4` square units

D

`8` square units

Text Solution

Verified by Experts

The correct Answer is:
B
Required area `= int_(0)^(2pi) sin x dx`
`= - cos x|_(0)^(2pi) = -cos2pi - (-cos 0)`
`= - cos (pi+pi) + 1 = -[-cospi] + 1`
`= +cos(pi/2 + pi/2) + 1 = sin '(pi)/(2) + 1 = 1 + 1= 2` sq. units
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NDA PREVIOUS YEARS-DEFINITE INTEGRATION & ITS APPLICATION-DIRECTIONS
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  4. What is int(-pi/2)^(pi/2) x sinx dx equal to ?

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  5. What is int(0)^(pi/2) ln(tanx) dx equal to ?

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  6. Find the area of the parabola y^2=4a xbounded by its latus rectum.

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  7. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is I equal to ?

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  8. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is int(0)^(pi)((pi-x)...

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  9. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is int(0)^(pi) (dx)/(1...

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  10. Consider is int(0)^(pi//2) ln (sinx)dx equal to ? What is int(0)^(pi...

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  11. Consider is int(0)^(pi//2) ln (sinx)dx equal to ? What is int(0)^(pi...

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  12. What is int(0)^(pi//2) (dx)/(a^(2) cos^(2) x+ b^(2) sin^(2) x) equal t...

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  13. The area of a triangle, whose verticles are (3,4) , (5,2) and the p...

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  14. प्रथम चतुर्थांश में वृत्त x^(2)+y^(2)=4, रेखा x=sqrt(3)y एवं x-अक्ष द...

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  15. Find the area of the region in the first quadrant enclosed by x-a xi s...

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  16. Consider the curves y= sin x and y = cos x. What is the area of the re...

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  17. Consider the curves y = sin x and y = cos x . What is the area of ...

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  18. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

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  19. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

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  20. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

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  21. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

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