evualate each definite integral. Fundamental theorem of Calculus. 1 antiderivati

Question

evualate each definite integral. Fundamental theorem of Calculus.
1 antiderivative 3 m^2(4m^3 + 2)^3 dm. The 1 and 3 is F(a) - F(b), which is F(1) - F(3). This shows the connection between antiderivatives and definite integrals. I cannot find the symbol for this. The 3(b) is on top and the 1(a) is on the bottom of the symbol. Hope this helps.
evualate each definite integral. Fundamental theorem of Calculus.
1 antiderivative 3 m^2(4m^3 + 2)^3 dm. The 1 and 3 is F(a) - F(b), which is F(1) - F(3). This shows the connection between antiderivatives and definite integrals. I cannot find the symbol for this. The 3(b) is on top and the 1(a) is on the bottom of the symbol. Hope this helps.

Explanation / Answer

If we use U substitution on the integral we have u=4m^3+2 So du= 12m^2 dm or dm= du/12m^2 Substituting in the original integrand we have m^2 (u)^3 du/12m^2. Simplifying we have 1/12 u^3 du. Antiderivative is 1/12*1/4 u^4 or 1/48 u^4. Substituting back we have 1/48 (4m^3+2)^4 from limits of 1 to 3. This computes as 1/48( 110)^4- 1/48 (6)^4 Since 110^4 is a pretty big number I'll leave it in this format.

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