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Integrate the following functions int...

Integrate the following functions
`int_(0)^(r ) (2x-x^(3)) dx `

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AI Generated Solution

To solve the integral \( \int_{0}^{r} (2x - x^3) \, dx \), we will follow these steps: ### Step 1: Break down the integral We can separate the integral into two parts: \[ \int_{0}^{r} (2x - x^3) \, dx = \int_{0}^{r} 2x \, dx - \int_{0}^{r} x^3 \, dx \] ...
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ICSE-VECTORS SCALARS ELEMENTARY CALCULUS -UNSOLVED PROBLEMS
  1. Integrate the following functions int(0)^(r ) (2x-x^(3)) dx

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  2. Differentiate the following w.r.t x 2020

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  3. Differentiate the following w.r.t x pi^(2)

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  4. Differentiate the following w.r.t x pie

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  5. Differentiate the following w.r.t x e^(-5)

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  6. Differentiate the following w.r.t x 16x^(8)

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  7. Differentiate the following w.r.t x x^(-4)

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  8. Differentiate the following w.r.t x x^(5//2)

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  9. Differentiate the following w.r.t x 4x^(3)-10 -6x^(2)

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  10. Differentiate the following w.r.t x x^(2) +3x +3/x

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  11. Differentiate the following w.r.t x tan(3x+1)

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  12. Differentiate the following w.r.t x cos 3x

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  13. Differentiate the following w.r.t x sqrt(sinx)

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  14. Differentiate the following w.r.t x 3x^(2)+12x - 11//x

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  15. Differentiate the following w.r.t x tan x+2 sin + 3 cos x - 1/2 lo...

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  16. Differentiate w.r.t x using product rule . (5x+2) (4-3x)

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  17. Differentiate w.r.t x using product rule . sqrt(x). sec x

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  18. Differentiate w.r.t x using product rule . (ax^(2)+bx+c)(x-d)

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  19. Differentiate w.r.t x using product rule . x^(3) sin x

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  20. Differentiate w.r.t x using product rule . x sin x log x

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  21. Differentiate w.r.t x using product rule . (1+ 2 tan x) ( 5+4 cos x)

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