1 of 8 0-day streak

Anti-differentiate a power of a linear function

Question 1 of 8

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G'(u)=-\frac{3}{2}\,\left(-2\,u - 1\right)^{-3}

\int -\frac{3}{2}\,\left(-2\,u - 1\right)^{-3}\,du

G(0)=\frac{37}{8}

Keep the original signed linear bracket unchanged in the primitive: do not expand, factor or rescale it. Enter exact values

Work on the connected interval containing the given input and excluding the zero of the bracket

(a)1 mark

Choose the anti-derivative family whose constant will be fixed by the condition

\int -\frac{3}{2}\,\left(-2\,u - 1\right)^{-3}\,du

G(u)=-\frac{3}{8}\,\left(-2\,u - 1\right)^{-2} + C

G(u)=\frac{3}{4}\,\left(-2\,u - 1\right)^{-2} + C

G(u)=-\frac{3}{8}\,\left(-2\,u - 1\right)^{-3} + C

G(u)=-\frac{3}{8}\,\left(-2\,u\right)^{-2} + C

(b)4 marks

Enter the exact coefficient, original bracket parts and new exponent

G(u)=\square\,\left(\square\,u + \square\right)^{\square} + C

Outer coefficient Coefficient of the variable in the bracket Constant in the bracket New exponent

Find the additive constant using the initial-value condition

G(0)=\frac{37}{8}

Additive constant C