document.write( "Question 1180435: The area of the region under the curve given by the function f(x) = 2x2 + 6 on the interval [0, b] is 36 square units, where b > 0.\r
\n" ); document.write( "\n" ); document.write( "The value of b is ?\r
\n" ); document.write( "\n" ); document.write( "a. 1
\n" ); document.write( "b. 2
\n" ); document.write( "c. 3
\n" ); document.write( "d. 4 \n" ); document.write( "

Algebra.Com's Answer #810090 by ikleyn(52879) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The area of the region under the curve given by the function f(x) = 2x2 + 6 on the interval [0, b] is 36 square units, where b > 0.
\n" ); document.write( "The value of b is ?
\n" ); document.write( "a. 1
\n" ); document.write( "b. 2
\n" ); document.write( "c. 3
\n" ); document.write( "d. 4
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The area under the curve is the integral of the given function from 0 to value of \"b\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This integral is equal to  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we need find \"b\" from equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 36,\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "     = 108.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The function on the left is monotonically increasing function of \"b\", \r\n" );
document.write( "\r\n" );
document.write( "so if we guess the value, it is the unique solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Easy guessing gives  b = 3 as the solution.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );