Use the first three non-zero terms of a Maclaurin series to estimate .

Question

Use the first three non-zero terms of a Maclaurin series to estimate  .

	0.747
	0.767
	0.757
	0.737

Answer 1

e^x = 1 + x + x²/2! + x³/3! + ...

So, e^{-x^2} = 1 + (-x²) + (-x²)²/2! + ... = 1 - x² + x⁴/2 - ...

Therefore, ∫_{(from 0 to 1)} e^{-x^2}dx = ∫_{(from 0 to 1)} [ 1 - x² + x⁴/2 ^-...]dx = x - x³/3 + x⁵/10 - ..._{(from 0 to 1)}

≈ 1 - 1/3 + 1/10 = 0.76666666 ≈ 0.767