The correct option is A M2(v^2 u^2) . ∫ _ u ^ v Mvdv =M∫ _ u ^ v vdv =M v ^ 2 2 | _ 0 ^ v = M 2 [ v ^ 2 u ^ 2 ] ...

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Standard VIII

Mathematics

Multiplication of Monomials

Evaluate: ∫u...

Question

Evaluate:
$\int_{u}^{v} M v d v$ .

\frac{M}{2} (v^{2} - u^{2})

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\frac{M}{2} (u^{2} - v^{2})

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\frac{M}{2} (v - u)

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\frac{M}{2} (u - v)

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Solution

The correct option is A $\frac{M}{2} (v^{2} - u^{2})$ .
$\int_{u}^{v} M v d v$
$= M \int_{u}^{v} v d v$
$= M \frac{v^{2}}{2} |_{0}^{v}$
$= \frac{M}{2} [v^{2} - u^{2}]$

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Evaluate:∫vuMv dv.

The correct option is A M2(v2−u2).∫vuMvdv=M∫vuvdv=Mv22|v0=M2[v2−u2]

Evaluate:
$\int_{u}^{v} M v d v$ .

The correct option is A $\frac{M}{2} (v^{2} - u^{2})$ .
$\int_{u}^{v} M v d v$
$= M \int_{u}^{v} v d v$
$= M \frac{v^{2}}{2} |_{0}^{v}$
$= \frac{M}{2} [v^{2} - u^{2}]$