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    dy/dx = sin²x
    When x = 0.1, y = 0.2. [Note: x and y are given in radians.]
    Find y = f(x) and evaluate any constants.

    Can someone explain another method to me excluding integration by parts.
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    (Original post by nas7232)
    dy/dx = sin²x
    When x = 0.1, y = 0.2. [Note: x and y are given in radians.]
    Find y = f(x) and evaluate any constants.

    Can someone explain another method to me excluding integration by parts.
    sin²x = 0.5 - 0.5Cos2x

    Then integrate that.
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    (Original post by nas7232)
    dy/dx = sin²x
    When x = 0.1, y = 0.2. [Note: x and y are given in radians.]
    Find y = f(x) and evaluate any constants.

    Can someone explain another method to me excluding integration by parts.
    

\cos 2x = 1-2\sin ^{2} x\\

\sin ^{2} x = \frac{1}{2}(1-\cos 2x)\\

y=\frac{1}{2}\int 1-\cos 2x dx \\

y=\frac{1}{2}[x-\frac{1}{2}\sin 2x]+C\\

y=\frac{1}{4}[2x-\sin 2x]+C\\

0.2=\frac{1}{4}[0.2-\sin 0.2] + C\\

\textit{You can find your constant and hence find y=f(x)}
 
 
 
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