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Evaluate egin{equation} rac{igint_{ rac{ p}{2}}^{2 p} (5 ext{sin }x - 3 ext{cos }x) ext{d}x}{} igg) ext{.} ewline The diagram in your answer booklet shows the graphs with equations $y = 5 ext{sin }x$ and $y = 3 ext{cos }x$, ext{ for } 0 ext{ ≤ } x ext{ ≤ } 2 ext{π} - Scottish Highers Maths - Question 11 - 2023
Question 11
Evaluate egin{equation} rac{igint_{ rac{ p}{2}}^{2 p} (5 ext{sin }x - 3 ext{cos }x) ext{d}x}{} igg) ext{.} ewline The diagram in your answer booklet shows th... show full transcript
Worked Solution & Example Answer:Evaluate egin{equation} rac{igint_{ rac{ p}{2}}^{2 p} (5 ext{sin }x - 3 ext{cos }x) ext{d}x}{} igg) ext{.} ewline The diagram in your answer booklet shows the graphs with equations $y = 5 ext{sin }x$ and $y = 3 ext{cos }x$, ext{ for } 0 ext{ ≤ } x ext{ ≤ } 2 ext{π} - Scottish Highers Maths - Question 11 - 2023
Step 1
Evaluate \( \int_{\frac{\pi}{2}}^{2\pi} (5\sin x - 3\cos x) \, dx \)
Answer
The area represented by the integral in (a) can be shaded on the diagram by locating the intersection points of the graphs of ( y = 5\sin x ) and ( y = 3\cos x ) within the specified limits and shading the area above the x-axis between the two curves from ( \frac{\pi}{2} ) to ( 2\pi ).