Verifying a Reduction Formula In Exercises 79-82, use
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Calculus
- sinx sinx +x The integral Cosx - e +e dr may be written as mensinxipr+ gerx 1 C. where m, n, p, q, r, and C are constants not equal to zero. Evaluate m +n+p+q+r. sinxarrow_forwardCalculus 1, 135:01-05, S20 Ant Quiz: Quiz 11 This Question: 3 pts 4 of 8 (2 complete) Evaluate the following integral using the Fundamental Theorem of Calculus. 12 | (5- x)(x- 12) dx 12 343 | (5- x)(x- 12) dx = 6 5 (Type an exact answer.) (ц) Morearrow_forwardProof Prove (Theorem 2.3) that d [x"] dx nx"-1 %3D for the case in which n is a rational number. (Hint: Write y = xP/4 in the form ya Assume that p and q are integers, where q > 0.) = xP and differentiate implicitly. > 0.)arrow_forward
- sinx +x +e COsr - e SInx The integral -dx may be written as me nsinx + px + geA +C, where m, n, p, q, r, and C are constants not sinx equal to zero. Evaluate m +n+p+q+r.arrow_forwardHow does y= sin x compare to y= cos x in terms of transformation (explain) convert • f(x) = Cos [2(x-π/2)] and f(x) = Cos (3x) To g(x) = Sin [b(x-h)] + karrow_forwardComplex analysis: Solve this integral using contour integration.arrow_forward
- Meteorology The normal monthly hightemperatures H (in degrees Fahrenheit) in Erie,Pennsylvania, are approximated byH(t) = 57.54 − 18.53 cos πt6 − 14.03 sin πt6and the normal monthly low temperatures L areapproximated byL(t) = 42.03 − 15.99 cos πt6 − 14.32 sin πt6where t is the time (in months), with t = 1 correspondingto January (see figure). (Source: NOAA)1 2 3 4 5 6 7 8 9 10 11 1220406080Month of yearTemperature(in degrees Fahrenheit)tL(t)H(t)(a) What is the period of each function?(b) During what part of the year is the difference betweenthe normal high and normal low temperaturesgreatest? When is it least?(c) The sun is northernmost in the sky around June 21,but the graph shows the warmest temperaturesat a later date. Approximate the lag time of thetemperatures relative to the position of the sun.arrow_forwardIntegral of cos2 Ө Evaluatearrow_forwardSubstitution review Derive integral formula 14 in Table 8.1: tan ax dx = -In|sec ax| + C. aarrow_forward
- sinx sinx +x +e cosx - e The integral dr may be written as mensinx +px+qe™ +C, where m, n, p, q, r, and C are constants not sinx equal to zero. Evaluate m +n+p+q+r. A -5 -1 (c) зarrow_forwardCalculus Evaluate there integral using a rationalizing substitution [² dx/(x² + x√√x)arrow_forwarddx Perform the Integrations 1+ sin x+cos x Use the editor to format your answerarrow_forward
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