Question
Suppose that $ f(1) = 2 $, $ f(4) = 7 $, $ f^\prime(1) = 5 $, $ f^\prime(4) = 3 $ and $ f^{\prime\prime} $ is continuous. Find the value of $ \displaystyle \int_1^4 x f^{\prime\prime} (x)\ dx $.
Step 1
We can apply the integration by parts formula, which is $\int u dv = uv - \int v du$. Here, we let $u = x$ and $dv = f^{\prime\prime}(x) dx$. Show more…
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Suppose that $f(1)=2, f(4)=7, f^{\prime}(1)=5, f^{\prime}(4)=3,$ and $f^{\prime \prime}$ is continuous. Find the value of $\int_{1}^{4} x f^{\prime \prime}(x) d x$
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$\begin{array}{l}{\text { Suppose that } f(1)=2, f(4)=7, f^{\prime}(1)=5, f^{\prime}(4)=3, \text { and }} \\ {f^{\prime \prime} \text { is continuous. Find the value of } \int_{1}^{4} x f^{\prime \prime}(x) d x}\end{array}$
Techniques of Integration
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