If # int_0^3 f(x) dx = 8 # then calculate? (A) (i) #int_0^3 2f(x) dx#, (ii) #int_0^3 f(x) + 2 dx# (B) #c# and #d# so that #int_c^d f(x-2) dx #
2 Answers
A) (i)
#int_0^3 \ 2f(x) \ dx = 16 #
A) (ii)#int_0^3 \ f(x) + 2 \ dx = 14 # B)
# c=2 # ;#d = 5 #
Explanation:
We are given that:
# int_0^3 \ f(x) \ dx = 8 #
Part (A)
(i)
#int_0^3 \ 2f(x) \ dx = 2 \ int_0^3 \ f(x) \ dx #
# " " = 2* 8 #
# " " = 16 # (ii)
#int_0^3 \ f(x) + 2 \ dx = int_0^3 \ f(x) \ dx + int_0^3 \ 2 \ dx #
# " " = int_0^3 \ f(x) \ dx + 2 \ int_0^3 \ dx #
# " " = 8 + 2[x]_0^3 #
# " " = 8 + 2(3-0) #
# " " = 8 + 6 #
# " " = 14 #
Part (B)
We are given that:
#int_c^d \ f(x-2) \ dx = 8 #
The graph of
Thus, as we know that
# c-2 = 0 => c=2 #
# d-2 = 3 => d = 5 #
Explanation:
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Enjoy Maths.!