+0  
 
0
453
6
avatar+1832 

 

I think it must be sin4(x-3) insted of cos4(x-3) in the last step ! 

 

 Feb 13, 2015

Best Answer 

 #5
avatar+27377 
+10

Yes, you could do, as there is a "c" to wrap up the constants (though you would change the cos term to a sin term as per your original question!)

 

.

 Feb 13, 2015
 #1
avatar+20850 
+10

I think it must be sin4(x-3) insted of cos4(x-3) in the last step !

Yes!

Because: $$\int{\cos(4u)}\ du = \frac{1}{4}\sin(4u)$$

.
 Feb 13, 2015
 #2
avatar+1832 
0

Also in this question, why they didn't wrote $$\frac{1}{2}(x+1)$$  insted of $$\frac{1}{2}x$$ ! 

 

 

 

 Feb 13, 2015
 #3
avatar+27377 
+10

$$\frac{1}{2}\int (1+\cos{2(x+1)})dx=\frac{1}{2}\int dx+\frac{1}{2}\int \cos{2(x+1)}dx$$

 

so the single x comes from the first integral on the right-hand side. However, you could add whatever constant you like, because, as it's an indefinite integral, any other constants are accounted for in the "c" at the end.

.

 Feb 13, 2015
 #4
avatar+1832 
0

So here can I wrote $$\frac{3}{8}x$$ insted of $$\frac{3}{8}(x-3)$$  ? 

 

 

 Feb 13, 2015
 #5
avatar+27377 
+10
Best Answer

Yes, you could do, as there is a "c" to wrap up the constants (though you would change the cos term to a sin term as per your original question!)

 

.

Alan Feb 13, 2015
 #6
avatar+1832 
+5

very clear

thank you Alan and heureka 

 Feb 13, 2015

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