Questions
ENGF0003_24-25 Activity 3.2: Pre-workshop Activity Set | Week 3: Integral Calculus (3 hours)
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Question textIntegrate {x\cdot \sqrt{2\cdot x-4}} with respect to {x} using the substitution u={2\cdot x-4}. [input] Your last answer was interpreted as follows: \[ \frac{1}{10}\cdot {\left(2\cdot x-4\right)}^{\frac{5}{2}}+\frac{2}{3}\cdot {\left(2\cdot x-4\right)}^{\frac{3}{2}}+c \]The variables found in your answer were: \( \left[ c , x \right]\) Check Question 19
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Step-by-Step Analysis
We start by identifying the integral to compute and the suggested substitution.
- The task is to integrate x * sqrt(2x - 4) with respect to x, using the substitution u = 2x - 4.
- Compute the differential: du = 2 dx, so dx = du/2. Also express x in terms of u: since u = 2x - 4, we have x = (u + 4) / 2.
Proceed with the substitution......Login to view full explanationLog in for full answers
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