Chapter 4: Integration

Section 4.4: Integration by Substitution

Example 4.4.6

Verify that ${\int }_{-\mathrm{\π}}^{\mathrm{\π}}\sin \left(x\right) \mathit{\ⅆ}x\=0$, and that ${\int }_{-\mathrm{\π}\/2}^{\mathrm{\π}\/2}\cos \left(x\right) \mathit{\ⅆ}x\=2{\int }_0^{\mathrm{\π}\/2}\cos \left(x\right) \mathit{\ⅆ}x$. Solution •  Control-drag the first integral. •  Context Panel: Evaluate and Display Inline ${\int }_{-\mathrm{\pi }}^{\mathrm{\pi }}\sin \left(x\right) \mathit{\ⅆ}x$ = $0$ •  Control-drag the second integral. •  Context Panel: Evaluate and Display Inline ${\int }_{-\mathrm{\pi }\/2}^{\mathrm{\pi }\/2}\cos \left(x\right) \mathit{\ⅆ}x$ = $2$ •  Control-drag the third integral. •  Context Panel: Evaluate and Display Inline $2{\int }_0^{\mathrm{\pi }\/2}\cos \left(x\right) \mathit{\ⅆ}x$ = $2$

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