What is the integral from-3/2 to-1 of (2x+3)^{100} ?

The integral from-3/2 to-1 of (2x+3)^{100} is 1/202

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integral from-3/2 to-1 of (2x+3)^{100}

\int_{- \frac{3}{2}}^{- 1} (2 x + 3)^{100} d x

\frac{1}{202}

Decimal

0.00495 \dots

Solution steps

\int_{- \frac{3}{2}}^{- 1} (2 x + 3)^{100} d x

Apply Integration By Parts

: [(2 x + 3)^{100} x - \int 200 (2 x + 3)^{99} x d x]_{- \frac{3}{2}}^{- 1}

= [(2 x + 3)^{100} x - \int 200 (2 x + 3)^{99} x d x]_{- \frac{3}{2}}^{- 1}

\int 200 (2 x + 3)^{99} x d x = 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100})

= [(2 x + 3)^{100} x - 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100})]_{- \frac{3}{2}}^{- 1}

Compute the boundaries:

\frac{1}{202}

= \frac{1}{202}

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What is the integral from-3/2 to-1 of (2x+3)^{100} ?
The integral from-3/2 to-1 of (2x+3)^{100} is 1/202