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13.

Use substitution to evaluate integral subscript 0 superscript straight pi over 2 end superscript sin 2 x square root of 4 plus 9 sin squared x end root space d x

Ans. 1/27(26 sq.rt 13-16 = 2.88 (ok)

12.

To the nearest two decimal places, calculate R subscript 5for f left parenthesis x right parenthesis equals x cubed plus 1on open square brackets 0 comma space 4 close square brackets.

Ans. 96.16