I can't quite understand your process, not being offensive but it looks a bit messy. (I prefer LaTeX more XD)
Checking your answer:∫7.523−x⋅10052⋅9⋅31,500,000 dx
Simplify & Pull the constant out:
=1,134,000,000∫7.523−xdx
Now solving: ∫3−xdx
Substitute u=−x, dx=−du
=−∫3udu
Apply exponential rule:
=−3uln(3)
Unsubstitude u:
−3−xln(3)
So: ∫3−xdx=−3−xln(3)
Therefore: ∫7.523−xdx=(−3−7.5ln(3))−(−3−2ln(3))
≈0.1009
Ans=0.1009⋅1,134,000,000
≈114420000(Joules)
(Wait a minute, why is my answer different from yours @_@)
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