Only one of these calculations is correct to evaluate the definite integral /sinx dx Using the Simpson's Rule with n=4 Select one: O None O = 12 (/sin(0) +4×/sin(t) +2× /sin(t/2) +4× /sin(t/3)+ /sin(t/4) ) (4x/sin(t/4) + 2x/sin(Tt/2) +4× /sin(31/4)) 8 180 -(4×/sin(t/4) + 2×/ sin(T/2) + 4×/sin(3t/4) ) 12 %3D (4x/ sin(T/4) + 2×/sin(T/2) +4x /sin(31/4) ) 12 O = (/sin(0) +4×/sin(t) +2× /sin(2t) +4× /sin(3t) + /sin(4Tt) ) 12

Determine the form that would make ſ sin (: cos () sin( 0) de integrable. CoS

A. f sin³x cos2x dx B. sin 2x cos 3x dx C. f 8 sin*x dx

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Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & %3D sin(A – B) = sinAcosB- cosAsinB cotAcotB+1 Verify that cot(A + B) cotB-cotA

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Evaluate the definite integral a) Find an anti-derivative I^V₂ b) Evaluate x² + 4x(x³ + 1) dx •√√₂ª + /x² + 4x(x³ + 1)dx= = Sª √x² + 4x(x³ + 1) de = If needed, round part b to 4 decimal places. +C

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What should we substitute for the integrand in /sin²4 x cos4x dx? 24 Z Select the correct answer below: 2 O(sin(2x)) ¹2 (+ sin(2x)) ² 12 (cos(2x)) ¹2 ( + cos(2x)) ² 12 O(+cos(2x)) ¹2 ( cos(2x))² (+cos(2x)) 24 (½-cos(2x)) ² (½-½ cos(2x))² (½-½ cos(2x)) 4 2 Content attribution W S #3 80 E D - $ 4 X C 999 R F % 5 V T MacBook Pro 6 G Y B ✓ & 7 H U * 00 8 N J A T K M

Only one of these calculations is correct to evaluate the definite integral sinx dx Using the Trapezoidal Rule with n=4 Select one: =(/sin(0) +2xV sin(T) +2x Vsin(t/2) +2x /sin(t/3)+ / sin(T/4) ) 8 "/sin(t/4) + V sin(T/2) + Vsin(3T/4) ) 4 (/sin(T/4) + /sin(Tt/2) + /sin(3n/4)) None /sin(0) +2x/sin(Tt) +2× /sin(2T1) +2× /sin(3T) + / sin(4Tt) ) 8 180 (/sin(t/4) + Vsin(t/2) + V sin(3I/4) ) 4