Question

Evaluate each of the following integrals Z 2z Je cos dz i. 4/ (Xcos (4x)dx 2 ii. tsin 2t dt ii Sy°cos 3ydy iv. 14x3-9х*+7х+3

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Answer #1

all these integrals are solved by using integration by parts

(x)np v(x)da)da dr u(a)v(x)da u(a) (r)dr​​Cas Zlz fd Lesing iategatin by pate 22 4 97 27 e e 16 Cos dz e 92 64 t gz &7 e Ce az e 16 27 e 64 GS 4 65 PSm ePage: T in 9 du im 1 2esinxdn asyxd 4 T2 4 Sm4To T) 2 Amoso sinlatt uhatitute -x gtdtdrtdtz day, tsinlatdt HSinlatt ndine dmPage: n (2t)ot 16 16 Jsin Catt int2ta) Cas Cas iny dy on pata - 219°7-Ces3y as 39 ay 3 10 sin3y 3 3 sin2y 2 3 40 2 3 3 40 dy40 Yo 4-04 Cas 80 40 2 8T 3 osimay V 7xt3)e-dm cng Tntention by pats: 3. -8utt -1 olr -Cn3943)e12x-18xt 7)e* +(24x-18) - (24e 2222t - (24x-18)e e 4x-9x2txe312x18x47 24x-18 +2 -e +3x 13x +16 43t3x2 e dn Auy

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