- #1

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- Homework Statement
- Show that ##\displaystyle\int_a^b\displaystyle\int_a^z \displaystyle\int_a^y f(x) dx dy dz = \displaystyle\int_a^b \frac{(b-x)^2}{2} f(x) dx ##

Hint: Think of how changing the order of integration in the triple integral changes the limits of integration.

- Relevant Equations
- No equation

If we solve the L.H.S. of this equation, we get ## \frac{(b-a)^3}{6}## and if we solve R.H.S. of this equation, we get ##-\frac{2b^3-3ba^2 +a^3}{6}##

So, how can we say, this equation is valid?

By the way, how can we use the hint given by the author here?

So, how can we say, this equation is valid?

By the way, how can we use the hint given by the author here?