Determine whether the integral is convergent or divergent. \int_0^2 32z^2 \ln z dz a)...

Question:

Determine whether the integral is convergent or divergent.

{eq}\int_0^2 32z^2 \ln z dz {/eq}

a) convergent

b) divergent

If it is convergent, evaluate it.

Definite Integration:

Let function {eq}r {/eq} is continous on {eq}[x,y] {/eq} and {eq}R {/eq} is a differentiable function on {eq}(x,y) {/eq} such that, {eq}\forall \,t \in (x,y),\,\frac{d}{{dt}}R(t) = r(t) {/eq} then,

{eq}\int\limits_x^y {r(t)dt = R(x) - R(y)} {/eq}.

The integrated function must be evaluated in both the extremes of the interval and subtract their values.

Answer and Explanation:

Given that: {eq}\displaystyle \int\limits_0^2 {32{z^2}\ln zdz} {/eq}

{eq}\displaystyle\ \eqalign{ & \int\limits_0^2 {32{z^2}\ln zdz} =...

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Definite Integrals: Definition

from Math 104: Calculus

Chapter 12 / Lesson 6
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