Chapter 4: Integration

Section 4.2: The Definite Integral

Example 4.2.2

$$ a)  Evaluate the definite integral of $2 \sin \left(x\right)\+3 \cos \left(x\right)$ on the interval $\left[0\,\mathrm{\π}\/2\right]$. b)  Verify that for this integrand the definite integral is a linear operator. $$ Solution $$ For part (a), write a single definite integral; for part (b), write a linear combination of two definite integrals. The results should be the same. $$ Part (a) •  Expression palette: Definite Integral template •  Context Panel: Evaluate and Display Inline ${\int }_0^{\mathrm{\π}\/2}\left(2 \sin \left(x\right)\+3 \cos \left(x\right)\right) \mathit{\ⅆ}x$ = $5$$$$$ Part (b) •  Expression palette: Definite Integral template •  Context Panel: Evaluate and Display Inline   $2{\int }_0^{\mathrm{\π}\/2}\sin \left(x\right) \mathit{\ⅆ}x\+3{\int }_0^{\mathrm{\π}\/2}\cos \left(x\right) \mathit{\ⅆ}x$ = $5$$$$$ $$

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