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This problem is from Chapter seven section to problem number
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twelve in the book Calculus Early Transcendental Sze, eighth
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Edition by James Store Here we have a definite integral
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from zero to a pie or two of parentheses to
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minus scientific data Square. So first thing we could
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do here is just evaluate this square and we have
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ah four minus for science data plus science. Where
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data Next, we can use an identity for Science
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Square. Richard, in a metric identity to rewrite
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this expression here, Sign square, and this becomes
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one minus coastline of two theater I'LL divided by two
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So here we could combine this four and one over
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two. Add those fractions together first to get it
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sign over too. Minus four. Signed data minus
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co. Sign of two data over to so we
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can evaluate each of these three girls. Oh,
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and it might help for this in a girl over
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here. The last general circled agreed to use the
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U substitution u equals today. So, evaluating the
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story we have a ninth eight over too. Plus
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for close on terra minus sign tooth data over two
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times two, which will give us a four and
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they're denominator. And we want to evaluate this new
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expression at zero and power too. So if we
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plug in pi over to first so co sign a
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pie or two zero and sign of two times pi
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over to a sign of pies also zero. So
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this is the first time we get after plugging in
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pi over too. And then when we plug in
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zero nine times here over to a zero four times
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coz I know zero is for and signer zeros also
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zero. So we're left with nine pi over four
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, minus four and that's our final answer.