Definite Integration Question 226
Question: The points of intersection of $ F_1(x)=\int_2^{x}{(2t-5)dt} $ and $ F_2(x)=\int_0^{x}{2tdt,} $ are
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Options:
A) $ ( \frac{6}{5},\frac{36}{25} ) $
B) $ ( \frac{2}{3},\frac{4}{9} ) $
C) $ ( \frac{1}{3},\frac{1}{9} ) $
D) $ ( \frac{1}{5},\frac{1}{25} ) $
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Answer:
Correct Answer: A
Solution:
Let $ F_1(x)=y_1=\int_2^{x}{(2t-5)dt} $ and $ F_2(x)=y_2=\int_0^{x}{2tdt} $
Now point of intersection means those point at which $ y_1=y_2=y\Rightarrow y_1=x^{2}-5x+6 $ and $ y_2=x^{2} $ .
On solving, we get $ x^{2}=x^{2}-5x+6\Rightarrow x=\frac{6}{5} $ and $ y=x^{2}=\frac{36}{25} $ . Thus point of intersection is $ ( \frac{6}{5},\frac{36}{25} ) $ .
BETA
