can someone remind me how to find definite integrals?

Question

anonymous · Answer

e.g. $$\int\limits_{4}^{9}(5z+2)dz$$

anonymous · Answer

Area under a space.

anonymous · Answer

rieman sum then?

anonymous · Answer

Romero's works if you can use calculator. Analytically, use the fundamental theorem of calculus part 2!

So for your example, antiderive 5z+2 -> (5(z^2)/2). Then evaluate that from 4 to g

(5(g^2)/2) - (5(4^2)/2)

anonymous · Answer

ok let me try to work it out and see what i get

anonymous · Answer

$$\int\limits_{0}^{5}( 5z+9)dz $$ this would be equal to 
$$5\int\limits_{0}^{5}z dz + 9\int\limits_{0}^{5}dz$$
$$5(z ^{2})2 + 9(z) = (5(5-0))/2 +9(5-0) = 25/2+ 45 =12.5+45 =6$$

anonymous · Answer

sorry 67.5

anonymous · Answer

got the answer on the key. thank you guys. appreciate the help

anonymous · Answer

@ipm1988  , the answer should be 107.5. You unfortunately applied the antiderivative and fundamental theorem incorrectly. 

the antiderivative of z is (z^2)/2....and you cant just evaluate by taking upper-lower in replacement for z. You need to replace upper, then subtract that entire evaluated value by the value gotten by the lower value.

anonymous · Answer

Puzzhang thanks for pointing out my mistake
:) I see it now I forgot to square

anonymous · Answer

@Puzzhang on your example you integrated the 5z but forgot the 2. I picked up on it and got what it should have been.

anonymous · Answer

aha that i did, whoops. Good you noticed it.