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# Evaluate $\begin{array}{l}F(x)=x^{9} \sec ^{2} x-3 x^{5} \sec ^{2} x+7 x^{3} \sec ^{2} x \\-x \sec ^{2} x+\sec ^{2} x \\F(-x)=-x^{9} \sec ^{2} x+3 x^{5} \sec ^{2} x-7 x^{3} \sec ^{2} x \\F(x)=-F(-x) \quad+x \sec ^{2} x+\sec ^{2} x \\F(x)+F(-x)=2 \sec ^{2} x \\2 \int_{0}^{\pi / 4} \sec ^{2} x d x \\2 \tan x]_{0}^{2 / 4} \\2[\tan (\pi / 4)-\tan 0] \\2[1-0]=2 \\\end{array}$

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 Question Text Evaluate $\begin{array}{l}F(x)=x^{9} \sec ^{2} x-3 x^{5} \sec ^{2} x+7 x^{3} \sec ^{2} x \\-x \sec ^{2} x+\sec ^{2} x \\F(-x)=-x^{9} \sec ^{2} x+3 x^{5} \sec ^{2} x-7 x^{3} \sec ^{2} x \\F(x)=-F(-x) \quad+x \sec ^{2} x+\sec ^{2} x \\F(x)+F(-x)=2 \sec ^{2} x \\2 \int_{0}^{\pi / 4} \sec ^{2} x d x \\2 \tan x]_{0}^{2 / 4} \\2[\tan (\pi / 4)-\tan 0] \\2[1-0]=2 \\\end{array}$ Updated On Feb 5, 2023 Topic Calculus Subject Mathematics Class Class 12 Passed Answer Type Video solution: 1 Upvotes 140 Avg. Video Duration 3 min
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