Other Math Archive: Questions from August 23, 2022
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Given \( y^{\prime}=\frac{4 x}{x^{2}+2} \) find \( y \) A. \( 4 x \ln \left|x^{2}+2\right|+c \) B. \( 4 \ln \left|x^{2}+2\right|+c \) C. \( 2 x \ln \left|x^{2}+2\right|+c \) D. \( 2 \ln \left|x^{2}+2\3 answers -
Given \( y=\int 3 x^{2}+2 d x \) and \( y \) passes through \( (0,1) \) find \( y \) A. \( y=6 x+c \) B. \( y=x^{3}+2 x+c \) C. \( y=6 x+1 \) D. \( y=x^{3}+2 x+1 \)1 answer -
Given \( y^{\prime}=3 \cos x+2 \sin x \), find \( y \). A. \( -3 \sin x+2 \cos x+c \) B. \( 3 \sin x-2 \cos x+c \) C. \( -3 \sin x-2 \cos x+c \) D. \( 3 \sin x+2 \cos x+c \)1 answer -
Find the anti-derivative of \( 12 \sin (4 x)(\cos 4 x)^{2} \) A. \( y=4 \cos ^{3} 4 x+c \) B. \( y=\cos ^{3} 4 x+c \) C. \( y=-\cos ^{3} 4 x+c \) D. \( y=4 \cos ^{3} 4 x+c \)3 answers -
Given \( y^{\prime}=\frac{4 x}{x^{2}+2} \) find \( y \). A. \( 4 x \ln \left|x^{2}+2\right|+c \) B. \( 4 \ln \left|x^{2}+2\right|+c \) C. \( 2 x \ln \left|x^{2}+2\right|+c \) D. \( 2 \ln \left|x^{2}+21 answer