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Computing Improper Integrals with an Undefined Endpoint

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Explanations 1

Previously, we found out that unbounded regions can, in fact, have finite area! So, a natural next step would be to try and calculate that area. This leads us into the notion of…
By Steven Kwon, Moor Xu, Alex Federspiel

Problems 3

∫041x dx=\int_0^4 \frac{1}{\sqrt{x}}\, \text{d}x =∫04x1dx=
∫011x3 dx=\int_0^1 \frac{1}{x^3} \, \text{d}x =∫01x31dx=
∫01ln⁡(x)dx=\int_0^1 \ln(x) \text{d}x =∫01ln(x)dx= (Hint: What is the derivative of xln⁡(x)x \ln(x)xln(x) with respect to xxx? Is there something you could add to that to make …