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Evaluate int(0)^(8) x^(5/3) dx...

Evaluate `int_(0)^(8) x^(5/3) dx`

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Verified by Experts

The correct Answer is:
4

Since PQ is of fixed length,
Area of `Delta PQR=(1)/(2)|PQ||RP|sintheta`
This will be maximum if `sintheta=1` and RP is maximum .
Since `y=mx+7` passes through `R'(0,7)` it must be rotated about (0,7) such that in new position, `theta` becomes `90^@` i.e., the line becomes perpendicular to `3x+4y+5=0`, then the slope of line `(4)/(3)`.
That is of `PR'=(4-7)/(4-0)=-(3)/(4)` = slope of given line. That is the in new position of the line. R coincides with R'.
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