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Question
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Solution
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 +bb (x + 4)`
= `int_0^2 dx/(-x^2 + x + 1/4 - bb(1/4) + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (bbsqrt17/2)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
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