Question 6 of 33beginner🔧 ApplyShort Answer2 marks

Find the following integrals in Exercises 6 to 20: ∫\int (2x - 3cos⁡\cos x + exe^{x}) dx

Correct Answer

x² - 3sin x + eˣ + C

Exercise: EXERCISE 7.1 | Q: 16 | (Page 10)
For More Understanding

Explanation

This is a straightforward integration problem using the property of linearity of integrals. Each term is integrated separately using standard formulas. The integral of xⁿ is xⁿ⁺¹/(n+1), the integral of cos x is sin x, and the integral of eˣ is eˣ itself. The constant of integration C is added at the end.

Solution Steps

  1. Step 1: Apply the property of linearity: ∫(2x - 3cos x + eˣ)dx = ∫2x dx - ∫3cos x dx + ∫eˣ dx

  2. Step 2: Integrate each term separately: ∫2x dx = 2 × x²/2 = x²

  3. Step 3: ∫3cos x dx = 3sin x (since integral of cos x is sin x)

  4. Step 4: ∫eˣ dx = eˣ (since integral of eˣ is eˣ)

  5. Step 5: Combine all results: x² - 3sin x + eˣ + C

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