As shown in class only, no othermethod will be allowed for credit,prove the theorem below. One of thestandards of proof, as for all proofsin this course, is that enough details,steps and explanation is provided sothat a reasonable person, readingthe proof for the first time, would beable to follow it.0sin3xdx11-x22dx232x2-1dxn=10121xdxmnmn02sinmxsinnxdx=002sin10xdxf(t)=sinatnthf(n)(t)Card[N]As shown in class and therequired reading, state and explainthe Atomic Hypothesis. No creditwill be given for saying that thingsare made of atoms. Also, explainwhy Grand Professor Feynman saysknowing Atomic Hypotheis issoimportant in the event of a disaster.Find the integral0sin3xdxFind the integral11-x22dxFind the integral232x2-1dxUse Simpson's rule for n=10toestimate the integral to six decimalsplaces121xdxProve that for all integers m and nwith m not equal ton that02sinmxsinnxdx=0Find the integral below in exactform, no decimals.02sin10xdxAs shown in class only, no othermethod will be allowed for credit,a. Compute the LaplaceTransform for f(t)=sinatin both of the two waysshown in class.b. Compute the LaplaceTransform for the nthderivative of a functionf(n)(t)As shown in class,a. State all the integraltransforms that were statedin class that were requiredtobe known. You must getall of them orno credit.b. State all the specialfunctions, along with theirdefinitions, that that werestated in class and that wererequired tobe known. Youmust get all of them ornocredit.