document.write( "Question 1004964: The problem is stated as: \r
\n" ); document.write( "\n" ); document.write( " $\"+%28d%2Fdx%29+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "I've done integral problems before but what is the purpose of the d/dx in front? that is throwing me off. I don't know what this problem needs in order to be solved. \r
\n" ); document.write( "\n" ); document.write( "Please help
\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #621298 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
If there are no x variables on either limit of integration, then the answer is simply 0. Here is why\r
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\n" ); document.write( "\n" ); document.write( "The value of $\"+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29\"$ is simply a constant. We don't need to know what actual constant it is, but we definitely know it is NOT a variable. It's a fixed number. So $\"+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29+=+C\"$ where C is a fixed number. The value of C is equal to the area under the curve from t = 0 to t = 2.\r
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\n" ); document.write( "\n" ); document.write( "Taking the derivative of any constant leads to 0. $\"+%28d%2Fdx%29+%28C%29+=+0\"$ . In a visual sense, all constant functions have graphs that are horizontal straight and flat lines. Any tangent line will have a slope of 0. So again, the derivative of a constant function is always 0.\r
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\n" ); document.write( "\n" ); document.write( "In the end, $\"+%28d%2Fdx%29+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29+=+0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Note: this only applies IF there are no x variables anywhere in the limits of integration. \n" ); document.write( "

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