1 of 8 0-day streak

Anti-differentiate a power of a linear function

Question 1 of 8

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

\int -\frac{1}{2}\,\left(3\,z - 1\right)^{-3}\,dz

F(-2)=-\frac{1175}{588}

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

Identify the family to which the required function belongs

\int -\frac{1}{2}\,\left(3\,z - 1\right)^{-3}\,dz

F(z)=\frac{1}{12}\,\left(3\,z - 1\right)^{-3} + C

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

F(z)=\frac{1}{12}\,\left(3\,z - 1\right)^{-2} + C

F(z)=\frac{1}{12}\,\left(3\,z\right)^{-2} + C

(b)4 marks

Enter the exact coefficient, original bracket parts and new exponent

F(z)=\square\,\left(\square\,z + \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 stated function-value condition

F(-2)=-\frac{1175}{588}

Additive constant C