86739 The value of the integral \(\int_{1}^{3}\left[x^{2}-2 x-2\right] d x\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is

86740 The value of \(\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\), where \([t]\) denotes the greatest integer \(\leq t\), is

86741 If the integral \(\int_{0}^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha, \beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}\) is equal to

86742 If \([x]\) denotes the greatest integer less than or equal to \(x\) then the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x]) d x\) is equal to

86743 The value of the definite integral
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \text { is equal to }\)

86739 The value of the integral \(\int_{1}^{3}\left[x^{2}-2 x-2\right] d x\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is

86740 The value of \(\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\), where \([t]\) denotes the greatest integer \(\leq t\), is

86741 If the integral \(\int_{0}^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha, \beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}\) is equal to

86742 If \([x]\) denotes the greatest integer less than or equal to \(x\) then the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x]) d x\) is equal to

86743 The value of the definite integral
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \text { is equal to }\)

86739 The value of the integral \(\int_{1}^{3}\left[x^{2}-2 x-2\right] d x\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is

86740 The value of \(\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\), where \([t]\) denotes the greatest integer \(\leq t\), is

86741 If the integral \(\int_{0}^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha, \beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}\) is equal to

86742 If \([x]\) denotes the greatest integer less than or equal to \(x\) then the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x]) d x\) is equal to

86743 The value of the definite integral
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \text { is equal to }\)

86739 The value of the integral \(\int_{1}^{3}\left[x^{2}-2 x-2\right] d x\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is

86740 The value of \(\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\), where \([t]\) denotes the greatest integer \(\leq t\), is

86741 If the integral \(\int_{0}^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha, \beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}\) is equal to

86742 If \([x]\) denotes the greatest integer less than or equal to \(x\) then the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x]) d x\) is equal to

86743 The value of the definite integral
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \text { is equal to }\)

86739 The value of the integral \(\int_{1}^{3}\left[x^{2}-2 x-2\right] d x\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is

86740 The value of \(\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\), where \([t]\) denotes the greatest integer \(\leq t\), is

86741 If the integral \(\int_{0}^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\) where \(\alpha, \beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}\) is equal to

86742 If \([x]\) denotes the greatest integer less than or equal to \(x\) then the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x]) d x\) is equal to

86743 The value of the definite integral
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \text { is equal to }\)