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Evaluate : int(-1)^2|x^3-x|\ dx...

Evaluate : `int_(-1)^2|x^3-x|\ dx`

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To evaluate the integral \( \int_{-1}^{2} |x^3 - x| \, dx \), we need to consider the absolute value function, which requires us to determine where the expression inside the absolute value changes sign. ### Step-by-step Solution: 1. **Identify the points where \( x^3 - x = 0 \)**: \[ x^3 - x = 0 \implies x(x^2 - 1) = 0 \implies x(x - 1)(x + 1) = 0 \] ...
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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. A die is thrown again and again until three sixes are obtained. Fin...

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  2. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  3. Evaluate : int(-1)^2|x^3-x|\ dx

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  4. Evaluate: int(5x-2)/(1+2x+3x^2)dx

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  5. Evaluate: int("sin"(x-a))/("sin"(x+a))dx

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  6. Differentiate the following function w.r.t. x : x^(sinx)+(sin x)^(...

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  7. If A is an invertible matrix of order 3\ and |A|=5, then find |a d...

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  8. If vec a\ xx\ vec b=\ vec c\ xx\ vec d\ and vec a\ xx\ vec c=\ ...

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  9. Find the value of lamda so that the lines (1-x)/(3)=(7y-14)/(2lamda)=(...

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  10. Solve the following differential equation: (dy)/(dx)+y=cosx-sinx

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  11. Find the particular solution, satisfying the given condition, for t...

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  12. By using properties of determinants, prove the following |(x+4,2x,2x),...

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  13. Write the vector equation of the following line: (x-5)/3=(y+4)/7=(6-z...

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  14. Using integration, find the area of the triangle ABC, coordinates o...

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  15. Find the area of circle 4x^2+4y^2=9 which is interior to the parabo...

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  16. If siny=sin(a+y),\ \ prove that (dy)/(dx)=(sin ^2\ (a+y))/(sina)

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  17. If (cos"x")^y=(sin y)^x , find (dy)/(dx)

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  18. Solve the following differential equation: ((x^2-1)dy)/(dx)+2x y=1/(x...

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  19. Solve the following differential equation: sqrt(1+x^2+y^2+x^2\ y^2)\ ...

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  20. If y=logtan(pi/4+x/2),\ show that (dy)/(dx)=secxdot Also find the ...

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