If we know $f(x)$, can we find $\int_{-1}^1 f(x^2-1) \:dx$?
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Ref: R5549

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Suggestion

A graph of the function $y=f(x)$ is sketched on the axes below;

the graph y equals f of x from x = -2 to 2, symmetrical about the y axis.

The value of $\displaystyle\int_{-1}^1 f(x^2-1) \:dx$ equals (a) $\dfrac{1}{4}\qquad$ (b) $\dfrac{1}{3}\quad \quad$ (c) $\dfrac{3}{5}\quad \quad$ (d) $\dfrac{2}{3}$.

Can we write down an equation for $f(x)$ for each distinct interval?

Can we then write down what $f(x^2-1)$ is?

If the values of $x$ run from $-1$ to $1$, what values does $x^2 -1$ run through?

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Calculus meets Functions

If we know $f(x)$, can we find $\int_{-1}^1 f(x^2-1) \:dx$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Suggestion

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If we know $f(x)$, can we find $\int_{-1}^1 f(x^2-1) \:dx$?
Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource