Question 5 of 33beginner🔧 ApplyShort Answer2 marks

Find the following integrals in Exercises 6 to 20: ∫\int (2x22x^{2} + exe^{x}) , dx

Correct Answer

2x33\frac{2x^3}{3} + exe^{x} + C

Exercise: EXERCISE 7.1 | Q: 9 | (Page 10)
For More Understanding

Explanation

This is a straightforward integration problem using basic integration rules. The integral can be split into two parts using the property that the integral of a sum equals the sum of integrals. For the polynomial term, the power rule is applied, and for the exponential term, we use the fact that the integral of exe^{x} is exe^{x} itself.

Solution Steps

  1. Step 1: Split the integral into two parts: ∫(2x² + eˣ) dx = ∫2x² dx + ∫eˣ dx

  2. Step 2: Apply the power rule to integrate 2x²: ∫2x² dx = 2 · x³/3 = 2x³/3

  3. Step 3: Integrate eˣ: ∫eˣ dx = eˣ (as shown in Example 19 of the context where ∫eˣ dx appears in the solution)

  4. Step 4: Combine both results: ∫(2x² + eˣ) dx = 2x³/3 + eˣ + C

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