Find the integral antiderivative for each of the following functions a Z 4cos

# Find the integral antiderivative for each of the

• Notes
• 138

This preview shows page 44 - 52 out of 138 pages.

Problem (6)Find the integral (antiderivative) for each of the following functions:(a)Z·4cosxsin2x¸dx,(b)Z¹2 cosx°px3ºdx.(c)Z1°cos2xcos2xdx,(d)Zx2/3¹x°4/3°3ºdx. Click Next to see the answer. ( a ) = 4 Z cot x csc xdx = ° 4 csc x + C . ( b ) = 2 Z ( cos x ) dx ° Z x 3 / 2 dx = 2 sin x ° 2 5 x 5 / 2 + C . Ziad Z. Adwan Lecture 15 & Lab 15 20 / 47
Test Your Understanding of the 7 Rules for Integration Problem (6)Find the integral (antiderivative) for each of the following functions:(a)Z·4cosxsin2x¸dx,(b)Z¹2 cosx°px3ºdx.(c)Z1°cos2xcos2xdx,(d)Zx2/3¹x°4/3°3ºdx. Click Next to see the answer. ( a ) = 4 Z cot x csc xdx = ° 4 csc x + C . ( b ) = 2 Z ( cos x ) dx ° Z x 3 / 2 dx = 2 sin x ° 2 5 x 5 / 2 + C . ( c ) = Z °² sec 2 x ³ ° 1 ± dx = tan x ° x + C . Ziad Z. Adwan Lecture 15 & Lab 15 20 / 47
Test Your Understanding of the 7 Rules for Integration Problem (6)Find the integral (antiderivative) for each of the following functions:(a)Z·4cosxsin2x¸dx,(b)Z¹2 cosx°px3ºdx.(c)Z1°cos2xcos2xdx,(d)Zx2/3¹x°4/3°3ºdx. Click Next to see the answer. ( a ) = 4 Z cot x csc xdx = ° 4 csc x + C . ( b ) = 2 Z ( cos x ) dx ° Z x 3 / 2 dx = 2 sin x ° 2 5 x 5 / 2 + C . ( c ) = Z °² sec 2 x ³ ° 1 ± dx = tan x ° x + C . ( d ) = Z ² x ° 2 / 3 ° 3 x 2 / 3 ³ dx = 3 3 p x ° 9 5 x 5 / 3 + C . Ziad Z. Adwan Lecture 15 & Lab 15 20 / 47
Test Your Understanding of the 7 Rules for Integration Problem (7)Find the integral (antiderivative) for each of the following functions:(a)Z(cosx)esinxdx,(b)Zcotx dx.(c)Ztanx dx,(d)Z°4x°2x2+x+4dx. Click Next to see the answer. Ziad Z. Adwan Lecture 15 & Lab 15 21 / 47
Test Your Understanding of the 7 Rules for Integration Problem (7)Find the integral (antiderivative) for each of the following functions:(a)Z(cosx)esinxdx,(b)Zcotx dx.(c)Ztanx dx,(d)Z°4x°2x2+x+4dx. Click Next to see the answer. ( a ) = e sin x + C . [Here, f ( x ) = sin x & so f 0 ( x ) = cos x . Then we use Z f 0 ( x ) e f ( x ) dx = e f ( x ) + C ]. Ziad Z. Adwan Lecture 15 & Lab 15 21 / 47
Test Your Understanding of the 7 Rules for Integration Problem (7)Find the integral (antiderivative) for each of the following functions:(a)Z(cosx)esinxdx,(b)Zcotx dx.(c)Ztanx dx,(d)Z°4x°2x2+x+4dx. Click Next to see the answer. ( a ) = e sin x + C . [Here, f ( x ) = sin x & so f 0 ( x ) = cos x . Then we use Z f 0 ( x ) e f ( x ) dx = e f ( x ) + C ]. ( b ) = Z cos x sin x dx = ln j sin x j + C . Which Rule are we using? Ziad Z. Adwan Lecture 15 & Lab 15 21 / 47
Test Your Understanding of the 7 Rules for Integration Problem (7)Find the integral (antiderivative) for each of the following functions:(a)Z(cosx)esinxdx,(b)Zcotx dx.(c)Ztanx dx,(d)Z°4x°2x2+x+4dx. Click Next to see the answer. ( a ) = e sin x + C . [Here, f ( x ) = sin x & so f 0 ( x ) = cos x . Then we use Z f 0 ( x ) e f ( x ) dx = e f ( x ) + C ]. ( b ) = Z cos x sin x dx = ln j sin x j + C . Which Rule are we using? ( c ) = Z sin x cos x dx = ° Z ( ° sin x ) cos x dx = ° ln j cos x j + C . Ziad Z. Adwan Lecture 15 & Lab 15 21 / 47
Test Your Understanding of the 7 Rules for Integration Problem (7) Find the integral (antiderivative) for each of the following functions: ( a ) Z ( cos x ) e sin x dx , ( b ) Z cot x dx .