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Integrate with respect to x: i) sin^(2)...

Integrate with respect to x: i) `sin^(2)x`, ii) `cos^(3)x` , iii) `sin2xcos3x`, iv) `1/(sqrt(x+3)-sqrt(x+2))`

Text Solution

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i) `x/2-1/4sin2x+C`, ii) `(sin3x)/(12) + 3/4sinx+C`
iii) `-1/10cos5x+1/2cosx+C`
iv) `2/3(x+3)^(3//2)+(9x+2)^(3//2)+C`
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Knowledge Check

  • Differentiate the following with respect to x. (i) sin 2x (ii) cos 3x (iii) tan 4x (iv) sin^3x (v) x^2//tan x

    A
    `2 cos 2x`, `- 3 sin 3x`
    B
    `2 cos 2x` , ` 3 sin 3x`
    C
    `2 cos 2x ,` `- 4 sin 3x`
    D
    `2 cos 2x`, ` 3 sinx`

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